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http://www.archive.org/details/essentialsoflogiOOsell 



THE ESSENTIALS OF 
LOGIC 



R. W. SELLARS, Ph.D. 

i » 

A ssistantProfessor of Philosophy 
University of Michigan 







BOSTON NEW YORK CHICAGO 

H&UGHTON MIFFLIN COMPANY 

(gfce BitacrjffiDe $zc& Cambridge 






CONTENTS 



I. Introductory 

A Definition of Logic — The Value of Logic — The Kinds 
of Logic — Introductory Logic — Relation of Logic to 
Other Sciences — The Material of Logic — References. 

II. The Nature and Setting of Thought . 

What is Thought? — Discovery and Proof — The Psy- 
chologist's View of Reasoning — Examples of Reasoning 

— The Conditions and Occasions of Thought — The Set- 
ting of Thought — Why we think — Processes Preliminary 
to Reflective Thought — Fact and Theory — Knowledge a 
Growth — References. 

III. About Terms 

The Unit of Thought — The Elements of the Proposition 

— Words and Terms — Kinds of Terms — Other Kinds of 
Terms — Connotation and Denotation — Synonyms for 
Connotation and Denotation — The Inverse Variation of 
Connotation and Denotation — Terms and Meaning — 
References. 

IV. The Use and Misuse of Language 

The Necessity for Language — Language and Analysis 

— The Logical Law of Language — Causes of Ambiguity 

— Univocal Words — Equivocal Words — Words change 
their Meanings — Vagueness — Abstract Terms particularly 
subject to Vagueness — Logic and Language — References. 

V. Classification and Division 

Classification and Classes — The Need for Classification 

— Types of Classification — Artificial Classification — Nat- 
ural Classifications — Natural Classification in the Light 
of Evolution — Character of Systematic Classification -— 
Classification and Division — Technical Terms used in 
Division — Rules of Division — Forms of Division — Di- 
chotomous Division — Classificatory Division — Dangers 
to be guarded against — References. 



COPYRIGHT, 1917, BY R. W SELLARS 



ALL RIGHTS RESERVED 



FEB -71917 ^ 



CAMBRIDGE . MASSACHUSETTS 



l<0 




CONTENTS 

I. Introductory 1 

A Definition of Logic — The Value of Logic — The Kinds 
of Logic — Introductory Logic — Relation of Logic to 
Other Sciences — The Material of Logic — References. 

II. The Nature and Setting of Thought ... 10 

What is Thought? — Discovery and Proof — The Psy- 
chologist's View of Reasoning — Examples of Reasoning 

— The Conditions and Occasions of Thought — The Set- 
ting of Thought — Why we think — Processes Preliminary 
to Reflective Thought — Fact and Theory — Knowledge a 
Growth — References. 

III. About Terms 27 

The Unit of Thought — The Elements of the Proposition 

— Words and Terms — Kinds of Terms — Other Kinds of 
Terms — Connotation and Denotation — Synonyms for 
Connotation and Denotation — The Inverse Variation of 
Connotation and Denotation — Terms and Meaning — 
References. 

IV. The Use and Misuse of Language ... 40 

The Necessity for Language — Language and Analysis 

— The Logical Law of Language — Causes of Ambiguity 

— Uni vocal Words — Equivocal Words — Words change 
their Meanings — Vagueness — Abstract Terms particularly 
subject to Vagueness — Logic and Language — References. 

V. Classification and Division 50 

Classification and Classes — The Need for Classification 

— Types of Classification — Artificial Classification — Nat- 
ural Classifications — Natural Classification in the Light 
of Evolution — Character of Systematic Classification — 
Classification and Division — Technical Terms used in 
Division — Rules of Division — Forms of Division — Di- 
chotomous Division — Classificatory Division — Dangers 
to be guarded against — References. 



iv CONTENTS 

VI. Principles of Definition 62 

Why Definition is needed — The Purpose and Nature of 
Definition — Logic stresses General Terms — Definition 
and Classification — The Verification of Meaning — Rules 
of Definition — Other Forms of Definition — The Pred- 
icates — The Importance of Definition — References. 

VII. Assertions and Propositions 76 

An Important Distinction — Critical vs. Uncritical As- 
sertion — What is an Assertion ? — Levels of Judgment — 
Concepts and Judgment — Judgment defined — All Knowl- 
edge Judgmental — The Part played by Language — The 
Logical Treatment of Propositions — References. 

VIII. The Logic of Propositions 89 

A General Division of Propositions — The Quality and 
Quantity of Propositions — Symbolic Classification of Prop- 
ositions — Reduction of Propositions to Logical Form — The 
Distribution of Terms — The Graphical Method — The Pur- 
pose of Logical Analysis — References. 

IX. The Implications of Propositions . . .98 

Immediate Inference — The Oppositions of the Four 
Kinds of Propositions — Conversion — Ob version — False 
Ob version — Contraposition — Significance of Immediate 
Inference — References. 

X. The Syllogism as a Mechanism .... 107 

The Nature of the Syllogism — An Analysis of the Syllo- 
gism — The Elements of the Syllogism — The Rules of the 
Syllogism — The Formal Syllogism and Actual Reasoning 
— References. 

XI. The Figures and Moods of the Syllogism . 118 

The Figures of the Syllogism — The Moods of the Syllo- 
gism — Reduction to the First Figure — Comparative 
Value of the Figures — References. 

XII. Abbreviated and Expanded Arguments — 

Extra-Syllogistic Arguments . . . .126 

Enthymeme — Prosyllogisms and Episyllogisms — Sori- 
tes — Extra-Syllogistic Arguments — References. 



/ 3 J 



CONTENTS v 

XIII. Hypothetical and Disjunctive Syllogisms . 132 

The Hypothetical Syllogism — The Rule of the Hypothet- 
ical Syllogism — The Fallacies of the Hypothetical Syllo- 
gism — Reduction to Categorical Form — The Disjunctive 
Syllogism — The Dilemma — References. 

XIV. Fallacies in Argumentation 141 

What a Fallacy is — A Classification of Fallacies — 
Classification of Deductive Fallacies — Fallacies of Equivo- 
cation — Fallacies of Unwarranted Assumption — Conclu- 
sion — References. 

XV. The Nature of Induction 159 

Induction and Deduction — A Glance at the History of 
Logic — The Function of the Syllogism — Why the Syl- 
logism is only a Part of Reasoning — Steps in Systematic 
Investigation — Three Elements in Investigation — The 
Problem of Generalization — The Implication of Generaliza- 
tion — How Generalization differs from Expectation — The 
Importance of Generalization — Testing Generalizations — 
References. 

XVI. The General Methods of Science . . . 173 

How Science developed — The Need of Analysis — The 
Value of Technique and Instruments — The Importance of 
Measurement — Experimentation — The Use of Experi- 
ment in Biology — Experimentation in Psychology — The 
Statistical Method — The Method of Graphs —The Func- 
tion of Hypotheses — References. 

XVII. Observation and Fact 184 

The Need of Observation — The Difficulty of securing 
Data — Conditions of Accurate Observation — Errors in 
Perception — Causes of Erroneous Perception — Summary 
for Perception — Observation in Everyday Life and in 
Science — Memory and Facts — Summary of Causes of 
Mistaken Memory — Testimony — Facts differ in Differ- 
ent Sciences — What are Relevant Facts? — References. 

XVIII. The Origin and Use of Hypotheses . . 197 

What is an Hypothesis? — Kinds of Hypotheses — Are 
Hypotheses Necessary for Science? — The Origin of Hy- 



211 



vi CONTENTS 

potheses — A Glance at the Psychology of Conjecture — The 
Value of Hypotheses — The Development of an Hypothesis 
— The Proof of an Hypothesis — Fact, Theory, and Hypoth- 
esis — Analogy as a Basis of Reasoning — False Analogy 

— References. 

XIX. The Discovery and Proof of Causal Rela- 

tions 

How Experience comes to us — What are Causal Connec- 
tions?— Post Hoc ergo Propter Hoc— MilYs Methods— The 
Method of Agreement — Examples of Induction by Agree- 
ment — The Character of the Method — Difficulties con- 
fronting the Method — The Method of Difference — Exam- 
ples of the Method — Warnings — The Method of Concom- 
itant Variations — Examples of the Method — Warning 

— The Joint Method of Agreement and Difference — Ex- 
amples — The Method of Residues — Examples — Re- 
marks on Mill's Method? — References. 

XX. Statistics . . . / 228 

The Nature of Statistics — Stages in Statistical Investi- 
gation — The Law of Statistical Regularity — Dangers in 
the Use of Statistics — The Value of Statistics — Refer- 
ences. 

XXI. Probability 239 

Abstract Laws vs. Concrete Events — Where Certainty is 
Possible — The Meaning of Probability — Probability and 
Chance — Three Kinds of Estimations — Empirical, or Non- 
Quantitative, Probability — Probabilities based on Averages 
— The Mathematical Treatment of Probability — Mistakes 
in interpreting Probabilities — References. 

XXII. Averages and Graphs 251 

The Uses of Averages — The Arithmetical Average — 
The ' Weighted ' Average —The Mode —The Median— The 
Geometric Average — The Comparative Advantages of 
these Averages — Graphs and Graphical Methods — 
References. 

XXIII. Testimony and Circumstantial Evidence . 264 

Scientific Investigation vs. Judicial Proof — The Difficul- 
ties confronting Judicial Proof — Distinction between Cir- 



CONTENTS vii 

cumstantial and Testimonial Evidence — The Nature of Cir- 
cumstantial Evidence — The Convergence of Evidence — 
Direct or Testimonial Evidence — The Modern Critical At- 
titude toward Testimony — Logical Standards and Tests 
— The Movement of Judicial Proof — The Massing of 
Mixed Evidence — References. 

XXIV. Explanation and System-Formation . . 278 

The Nature of Explanation — The Sentiment of Ration- 
ality — The Role of Concepts — Proof and Explanation — 
Systems are tentative — Levels of Explanation — General 
Explanation and Specific Explanation — Typical Systems 
of Knowledge — References. 

XXV. Truth and its Tests 294 

Back to the Definition of Logic — The Nature of Con- 
sistent Thinking — The Laws of Thought — The Postu- 
lates of Logic — The Question of Truth — The Criteria of 
Truth — Degrees of Belief — What the Attainment of 
True Ideas implies — The Meaning of Truth — ■ Truth and 
the Will to Believe — The Logic of Doubt — References. 

Questions and Exercises 311 

Index 345 



THE ESSENTIALS OF LOGIC 

CHAPTER I 

INTRODUCTORY 

A Definition of Logic. Logic may be defined as 
the science of the principles and conditions of connect 
thinking. To the beginner, a definition serves mainly 
as a guide-post to direct his attention to the general 
character of the subject which he is about to study. The 
above definition should therefore be taken merely as an 
indication of the field. The terms of which it is com- 
posed will gather content and meaning as the various 
topics are covered. Toward the end of the course, it is 
to be hoped that the student will be able to come back 
to the definition with a fuller grasp of its significance. 

Logic is a science in the sense that it is organized 
knowledge involving principles. The various sciences 
have different fields for investigation, but all of them 
agree in their purpose, which is the establishment of 
satisfactory information bound together and illuminated 
by laws. Thus, physics studies the most general charac- 
teristics of the physical world and seeks to reduce to 
order and interpret the facts it discovers ; botany ex- 
amines the structures, functions, and histories of plants ; 
and psychology gives its attention to the behavior of 
creatures possessing consciousness. All these sciences 
seek to replace the loose and hazy notions of popular 
thought by exact and systematic knowledge. Now logic 



2 THE ESSENTIALS OF LOGIC 

has the same purpose, but its field is peculiar. It can- 
not be classed among the physical sciences which de- 
pend upon perception and measurement, nor among the 
biological sciences, nor, finally, among the social sciences. 
In a very real sense modern logic presupposes all these 
sciences and is somehow a science at second remove 
from things. It is a science about the mental aspect of 
the sciences. The mediaeval logicians pointed out that the 
mind first ' intends,' or directs itself upon, the exter- 
nal world, and that only afterwards does it direct itself 
upon the mental processes and methods it has used. We 
may say, then, that logic involves a thinking about 
thinking. 

Because man is naturally outward-looking and de- 
sirous of practical results he is seldom clearly conscious 
of his methods and of the mental processes involved in 
thinking. It requires an effort for him to take this new 
attitude and to think about thinking, about those mental 
operations which make knowledge possible. But when 
he does so, he finds that the mind does work in an 
orderly fashion. It is the nature of this orderliness that 
logic seeks to bring into clear consciousness. 

The Value of Logic. So far as logic is a pure 
science, its value is essentially of the same kind as that 
of any other pure science. It satisfies an intellectual 
curiosity, a desire to know. Before a teacher can appeal 
strongly to such a value, the student must have expe- 
rienced it; at some past time he must have forgotten 
himself as an individual with private ambitions in the 
enjoyment of seeing problems solved, of watching mean- 
ing replace confusion ; he must have felt pleasure in 
knowledge for its own sake. The logician who is loyal 



INTRODUCTORY 3 

to his subject because he has faith in it asserts that logic 
has a value as a pure science, that man likes to know 
the working of his own mind just as he likes to know 
the laws of celestial mechanics. Why not, indeed? Is 
not the mind the supreme instrument which all must 
employ? 

But a pure science need not lack practical value. 
Logic is not only a pure science, but also an art or an 
applied science. An applied science is one which is able 
to work out suggestions and rules based on a broad study 
of the field involved. Looked at from this angle, logic 
may be considered " a free study of some of the chief 
risks of error in reasoning." 1 What logic can do for an 
individual is to render him conscious of the best meth- 
ods and the main difficulties in the various stages of 
actual thinking so that he will be more exacting in his 
mental operations. It should put him on his guard 
against dangers. It calls his attention incessantly to the 
value of clear and unambiguous ideas and to the proper 
level of scrutiny to be maintained before a fact is ac- 
cepted, an inference drawn, or a proposition admitted 
as a premise in reasoning. The mind is an instrument, 
and it should be polished instead of being left in a state 
of nature. It is true that the exigencies of life force us 
to be critical, but such criticism is too rough-and-ready 
to be entirely satisfactory. Is there good reason to doubt 
that care of the mind will pay at least as much as care 
of the body? There are good mental habits just as there 
are good physical habits; and neither comes without 
effort and reflection. "Its [logic's] practical value in 
general education is firstly this : that it demands very 

1 Sidgwick, Elementary Logic, p. 8, Introduction. 



4 THE ESSENTIALS OF LOGIC 

careful and exact thinking about its own subject-matter, 
and thus tends to produce a habit of similar carefulness 
in the study of any other subject. In this it only does 
for the mind what a thorough training in any other 
science might do. Secondly, it makes us realize better 
what the general forms of speech that we habitually use 
really mean, and familiarizes us with the task of examin- 
ing our reasonings and looking to see whether they are 
conclusive. In this it has an effect which the study of 
some special science like botany is not equally calcu- 
lated to produce. Thirdly, it brings into clearer con- 
sciousness, as aforesaid, our ideal of what knowing is, 
and so furnishes us with a sort of negative standard ; it 
makes us more alive to shortcomings in our ordinary 
opinions. But its chief value lies in its bearing upon 
those ultimate problems, concerning the nature of real- 
ity, and man's place and destiny in the world, from 
which at first sight it might seem far remote." l 

If logic can do even a part of this, it justifies itself 
as a practical study. While logic does not create new 
capacities in the mind of an individual, it helps to train 
and sharpen the capacities already there. 

The Kinds of Logic. Logic is one of the oldest of 
the sciences and has had a varied history. The result 
has been the growth of different branches emphasizing 
different aspects of thinking and somewhat different in- 
terpretations of the aim of logic. At times, these ' kinds 
of logic' have seemed opposed to one another, but, of 
late, they are seen to supplement one another and to 
make logic a broader investigation than it would have 
been without this branching. One kind of logic (exact 

1 Joseph, An Introduction to Logic, p. 10. 



INTRODUCTORY 5 

or symbolic) seeks to assimilate itself to mathematics 
in its methods ; another (concrete) stresses its relation 
to general philosophy, especially to theory of knowl- 
edge ; another (empirical or inductive) lays its emphasis 
upon the methods of the experimental and observational 
sciences. Back of these historically and linking itself 
with them in various ways — sometimes welcomed, some- 
times an outcast — is what is called 'Formal Logic/ 
We shall have a better idea of the limitations of Formal 
Logic as we cover various topics such as the 6 syllogism,' 
4 immediate inference,' and the 'logical form' of state- 
ments. Certain doctrines and technicalities must be dis- 
cussed and given as true and adequate a setting as pos- 
sible. They have their value, though this value must 
not be overestimated. 

Introductory Logic. The Introductory Logic of 
to-day in America seeks to organize together the essen- 
tials of the various kinds of logic. It retains as much 
of Formal Logic as seems valuable and combines it with 
a concreter study of actual thinking with a view to de- 
termine the principles and conditions of correct think- 
ing. In this effort, it has been aided immensely by the 
growth of psychology and philosophy, and the increasing 
reflection, by scientists themselves, upon their methods. 
Logic has acquired a new lease of life and is genuinely 
growing. More is known about thinking than ever be- 
fore, and this added knowledge has stimulated logic to 
break away from formalities. Yet logic has a rich in- 
heritance from the past which must not be belittled. 
What is needed is a new perspective and a more vital 
setting. We want to know the structure of our actual 
thinking so as to guard against the risks of error. 



6 THE ESSENTIALS OF LOGIC 

Relation of Logic to Other Sciences. The sciences 
most closely related to logic are rhetoric and psychology. 
The connection with psychology is obvious and we must 
examine it in some detail. But first let us examine its 
relation to grammar and rhetoric. 

Thinking is intimately bound up with language; 
language is, in fact, a necessary instrument to any sus- 
tained thinking which involves general ideas. For gram- 
mar, language is itself the subject-matter; for logic, it 
is the instrument of thought. The function of words 
is the fixation of meanings in our own mind and their 
suggestion to others. In another chapter we shall discuss 
the relation between thought and language. At present 
we only wish to point out that the law of language 
under its logical aspect is that of non-ambiguity . State- 
ments must, so far as possible, be clear as regards their 
significance. Accuracy and appropriateness in the use 
of words go hand in hand with the discrimination of 
ideas. 

Rhetoric is more nearly akin to logic than is gram- 
mar. While grammar treats of words largely apart 
from their meanings, rhetoric concerns itself with the 
expression of thought. Such expression is studied in 
relation to the purpose in hand, which may be expo- 
sition, description, argumentation or persuasion. It is 
impossible to draw any hard-and-fast line between these 
disciplines, for each is influenced by the results of the 
other ; we may say, however, that to-day both rhetoric 
and logic presuppose grammar as a preliminary and dif- 
fer from each other in that which they stress. Logic is 
more interested in the meaning which is expressed, 
its implications, foundation, and validity, than in the 



INTRODUCTORY 7 

mode or style in which it is expressed. Rhetoric, on 
the other hand, culminates in the artistic use of lan- 
guage. The fact that language is a necessary instrument 
of thought brings these disciplines together ; but logic 
has wider relations because thought is greater than its 
instrument. Language is, after all, a tool. 

The logician reflects upon the mental processes by 
means of which knowledge is achieved and naturally 
finds much assistance in psychology. So far as he in- 
vestigates how the individual thinks and the conditions 
of this thinking, he works hand in hand with the psy- 
chologist. Both examine perception, conception, judg- 
ment and reasoning and reach harmonious conclusions. 
The main difference between them is that psychology 
concerns itself more with the mental content, while 
logic stresses the value of the product. Just because 
the mind is a unity, it is impossible to find other than 
a working distinction between them due to a division 
of labor. They overlap, then, in the higher mental pro- 
cesses, and logic passes on to a study of the structure 
of knowledge and its validity, while psychology con- 
cerns itself with the structure of consciousness, its rela- 
tion to conduct, and its physiological conditions and 
concomitants. The logician has the right to make use 
of the knowledge psychology has achieved which bears 
upon his own task. Their relation should be one of 
mutual helpfulness. 

The Material of Logic. All sciences are objective ; 
that is, they consist of recognized facts and of princi- 
ples which organize and interpret these facts. Now, 
logic is, as we have already pointed out, a science about 
the sciences. It is interested in the nature of proof and 



8 THE ESSENTIALS OF LOGIC 

the laws of evidence ; it desires to see hoio knowledge 
is built up and how the parts of knowledge depend 
upon one another. This interest cannot be satisfied by- 
introspection alone, but requires a close study of the 
various sciences. In these it finds knowledge, and in 
their history the record of the steps by which it was 
obtained. We may say, then, that the material of logic 
is to be found in generally accepted knowledge and 
that this is approached with the purpose of discovering 
the processes involved. Knowledge is the material of 
logic much as the organism is the material of the 
biologist and the inorganic world the material of the 
physicist. 

Inductive logic has always paid close attention to the 
sciences which have so splendidly developed since the 
Renaissance. It is an attempt to formulate the methods 
which grew up unconsciously, or largely unconsciously, 
in this new and wonderful extension of human knowl- 
edge. The assumption controlling the series of inves- 
tigations which have given us the inductive branch of 
logic has been very well expressed by Whewell : " We 
may best hope to understand the nature and conditions 
of real knowledge by studying the nature and condi- 
tions of the most certain knowledge which we pos- 
sess ; and we are most likely to learn the best methods 
of discovering truth by examining how truths, now uni- 
versally recognized, have really been discovered." 1 

BuF logic must concern itself with all sorts of think- 
ing, with the conversations of daily life, with the argu- 
ments to be found in the social sciences, in political 
speeches, in essays, in editorials ; otherwise, it is apt to 

1 Whewell, History of Scientific Ideas (3d ed.),vol. I, p. 4. 



INTRODUCTORY 9 

become too formal and pedantic and to lose touch with 
the flexibility and variety of actual thought. There is 
another reason why the logician puts this emphasis on 
less specialized thinking and refuses to let it be elbowed 
away by the more technical levels of thought. We can 
know what thinking is only by thinking ourselves and 
then retracing our steps in memory to see exactly what 
we have been doing. The material of logic can be found 
ultimately only in consciousness. And, if the subject- 
matter is to be realized and really reflected upon, it 
must be reproduced and revivified in our own thought. 
But it is not always easy to do this with past thinking 
when this is technical and has an atmosphere of its 
own. And, when all is said, familiar thinking illustrates 
the essentials of the thinking process. Any one who 
studies logic seriously must be willing to think for him- 
self and to think about his thinking. 

REFERENCES 

Creighton, An Introductory Logic, chap. I. 
Sigwart, Logic, vol. I, General Introduction. 
Joseph, An Introduction to Logic, chap. I. 
Sidgwick, Elementary Logic, Introduction. 
Schiller, Formal Logic, chap. I. 



CHAPTER II 

THE NATURE AND SETTING OF THOUGHT 

What is Thought ? Thinking is the central opera- 
tion for logic. It is the operation which underlies 
knowledge and opinion and makes them possible. It 
behooves us, therefore, to gain as clear an idea of its 
nature and conditions as we can. If it is affected by 
mental habits, we want to know what are the best hab- 
its ; if it is controlled by feeling and emotion, we 
want to know how to lessen such control. In short, 
we wish to study the ways in which the human mind 
assimilates and develops knowledge — especially that 
knowledge which is called true. 

It is not easy to define that mental process desig- 
nated thinking. " No words are of tener on our lips 
than thinking and thought. So profuse and varied, in- 
deed, is our use of these words that it is not easy to 
define just what we mean by them. Assistance may 
be had by considering some typical ways in which the 
terms are employed. In the first place, thought is used 
broadly, not to say loosely. Everything that comes 
to mind, that 'goes through our heads,' is called a 
thought. To think of a thing is just to be conscious 
of it in any way whatsoever. Second, the term is re- 
stricted by excluding whatever is directly presented ; 
we think (or think of) only such things as we do not 
directly see, hear, smell, or taste. Then, third, the 
meaning is further limited to beliefs that rest upon 



THE NATURE AND SETTING OF THOUGHT 11 

some kind of evidence or testimony. Of this third type, 
two kinds — or, rather, two degrees — must be dis- 
criminated. In some cases, a belief is accepted with 
slight or almost no attempt to state the grounds that 
support it. In other cases, the ground or basis for a 
belief is deliberately sought and its adequacy to sup- 
port the belief examined. This process is called reflec- 
tive thought." 1 Now, logic is chiefly interested in this 
higher level of thinking where ideas are under control 
and organized in relation to one another. In fact, many 
logicians define logic as the science of proof or evidence. 

Certain terms are used by logicians as practically 
synonymous. Thus we shall have occasion to speak of 
reflective thought, reasoning, and inference at various 
times. These processes are much the same, though the 
context will show slight differences of emphasis. Tak- 
ing them as essentially the same, our present task is to 
find out what is the nature of the mental operation 
involved. What do we do when we reason or infer? 
What we want now is a suggestion of the general char- 
acter of the operation, leaving it to later chapters to 
study the various steps in methodical reasoning. 

Discovery and Proof. There are two parts to any 
complete act of reasoning, discovery, and proof. We 
reason when we are confronted by problems, by unfore- 
seen situations to which our habits and usual ideas 
are not immediately applicable. We are, as we say, at 
a loss ; we don't know what to think or to do. But this 
perplexity lasts for a time only. We make shift to size 
up the situation, to compare it with what in the past 
seems most like it, to analyze the various features, and 

1 Dewey, How We Think, pp. 1-2. 



12 THE ESSENTIALS OF LOGIC 

so on, until some idea suggests itself as a possible solu- 
tion. Such is the stage of tentative discovery. But 
another stage immediately sets in. The suggested solu- 
tion must be tested or proved. In practical affairs, this 
proving consists, in the main, of overt action. The 
new idea is tried out to see whether it will work. The 
proud possessor of a new auto finds himself compelled 
to reason in this rough-and-ready way only too often. 
This practical level of reasoning is sometimes called 
4 trial-and-error.' The process is familiar to all. 

In more theoretical reasoning, both the stage of dis- 
covery and the stage of proof are reflective. The sci- 
entist who makes a discovery has, as a rule, long 
brooded over the problem. The idea of universal gravi- 
tation did not come to Newton as a mere chance 
thought ; his mind was ripe for it. Archimedes had 
long been pondering over his particular problem before 
he took his famous bath and discovered the principle of 
specific gravity. But after the brilliant idea has sug- 
gested itself, it must be proved in the light of the facts. 
It must be shown to follow from certain premises or 
data; it must be guaranteed by its reasons or grounds. 
And this second task is often the more perplexing of 
the two. By proof we mean the process of establishing 
an idea on a firm intellectual foundation. Newton had 
to work out the method of fluxions and make delicate 
calculations on the basis of known measurements before 
he could consider his hypothesis reasonably proved, 
while Darwin had to make numerous experiments and 
collect data of the most varied kinds before he was 
willing to publish his theory. Proof must be considered 
a very important part of reasoning. Scrupulousness in 



THE NATURE AND SETTING OF THOUGHT 13 

regard to its standards is the sign of a trained mind. 
It is not too much to say that logic is primarily the 
science of proof. The question before the logician's 
mind is, 'Is such and such a given conclusion war- 
ranted ? ' Logic is retrospective and probative. 

The Psychologist's View of Reasoning. In the 
preceding chapter, we came to the conclusion that logic 
and psychology overlap, that no hard-and-fast line can 
be drawn between them. It may be of interest, there- 
fore, to examine the psychologist's view of reasoning. 
"To define reasoning fully it must be distinguished 
from imagination and memory when observed from the 
inside, and from instinct and habit when expressed in 
action. Reasoning may be distinguished from memory 
and imagination, not so much by the character of the 
mental states or by the way that they are obtained, 
as by the attitude that is taken toward them when they 
arise. The idea that is attained by reasoning may be 
exactly like an idea that on other occasions or by 
another man is merely remembered. The laws that 
govern the appearance of rational ideas are the laws of 
association, controlled in the same way as in memory 
and imagination. The important differences are : that 
the results of reasoning are new and are accepted as 
true ; the results of memory are true, but not new ; 
and the results of imagination are new, but not true" 1 
It is well to bear these contrasts in mind. Reasoning is 
a mental process taking some time to occur and con- 
trolled by the purpose of reaching accepted results. 
The logician makes the further demand that these re- 
sults be established by relation to their ground. 

1 Pillsbury, Essentials of Psychology, p. 217. 



14 THE ESSENTIALS OF LOGIC 

Examples of Reasoning. Let us take a case of 
reasoning in regard to heavenly phenomena which was 
made quite early in the history of civilization. Man 
soon discovered that a shadow was caused by the inter- 
vention of an opaque body between a source of light 
and a distant surface. He did not know exactly what 
took place, but he knew that the light was cut off from 
the region back of the opaque body. Thus he arrived 
at the universal proposition, * All shadows are caused 
by the intervention of an opaque body.' But an eclipse 
was soon recognized to be a case of shadow. Hence an 
opaque body must have intervened between the earth 
and the source of light. Here is a case of reasoning in 
which the conclusion is reached by resemblance or anal- 
ogy. An eclipse is a case of the intervention of an 
opaque body because it is a case of shadow. This 
reasoning contains the ground. Let us now examine a 
case of bad reasoning. " According to some accounts, 
the wise men of Spain argued with Columbus that he 
could not reach India by sailing west, because if the 
earth were round, as he asserted, he would at some 
time reach a point where the ship would be going down- 
hill and ultimately fall off, just as a minature vessel 
would fall, if it should attempt to travel around an 
artificial globe. If A is true (earth round), B must be 
true (circumnavigation impossible). If there is a re- 
semblance between earth and artificial globe in contour 
of surface, there must be a further resemblance, so it 
was held, in the relation of each to the objects upon 
its surface. ... In making their comparison, the wise 
men overlooked an important point of difference, viz., 
that for an object on the artificial globe the point 



THE NATURE AND SETTING OF THOUGHT 15 

towards which it gravitates is outside the globe, while 
for objects on the earth this point is within the earth 
itself." 1 

Thinking may be more or less conscious and more or 
less methodical. Logic seeks to induce individuals to 
take thinking seriously, to make their thinking method- 
ical and reflective. Especially does it stress evidence. 
Reflective thought is careful, and evidence-loving. It 
notes all the facts which can be thought to have bear- 
ing upon the problem and tests any conclusion by its 
consequences. 

The Conditions and Occasions of Thought. Re- 
flective thought or reasoning rests upon and grows out 
of experience. It has its causes and conditions. Thought 
does not arise just for no reason at all, but has its 
definite conditions. These reasons for thinking can be 
classified as social and personal. 

The stimuli which lead individuals to think usually 
come from the social environment. The pity is that 
this environment is so moderately stimulating. The 
more there is the spirit of intellectual and social adven- 
ture, the more alive will men be. When the environ- 
ment favors tradition and mere repetition and imitation, 
comparatively little vital and creative thinking is done. 
Life takes on the aspect of routine and habit, and 
classification of a formal kind overshadows discovery. 
Actions are repeated in the customary grooves, and no 
attempt is made to better them. There are periods, as 
during certain parts of the Middle Ages, when this 
social attitude is largely dominant. At such times, be- 
liefs are handed down by tradition and are not criti- 
1 Bode, An Outline of Logic, pp. 2-3. 



16 THE ESSENTIALS OF LOGIC 

cally examined. Such an atmosphere is not favorable 
to thinking. The individual is not taught to analyze 
and observe, to doubt and to form hypotheses. Thus, 
there is a sociology of logic, or, rather, logic has its 
social aspects which must not be lost sight of. Let me, 
by means of an example, contrast the lethargy of thought 
during the later Middle Ages with the eager spirit of 
science at its best. 

It is said that Francesco Sizzi, a Florentine astrono- 
mer, argued against Galileo's discovery of a new planet 
in the following way : — 

" There are seven windows in the head : two nostrils, 
two eyes, two ears, and a mouth ; so in the heavens 
there are two favorable stars, two unpropitious, two 
luminaries, and Mercury alone undecided and indiffer- 
ent. From which and many other similar phenomena 
of nature, such as the seven metals, etc., which it were 
tedious to enumerate, we gather that the number of 
planets is necessarily seven. 

" Moreover, the satellites are invisible to the naked 
eye, and therefore can have no influence on the earth, 
and therefore would be useless, and therefore do not 
exist. 

" Besides, the Jews and other ancient nations as well 
as modern Europeans have adopted the division of the 
week into seven days and have named them from the 
seven planets ; now, if w r e increase the number of the 
planets this whole system falls to the ground." 1 

The present is, on the whole, a period of skepticism 
and inquiry. The individual is taught to think for him- 
self, along certain lines at least, and not to accept ideas 

1 Lodge, Pioneers of Science, p. 106. 



THE NATURE AND SETTING OF THOUGHT 17 

unless he has pretty assured evidence for them. This 
social atmosphere, encouraging to thought, is a very- 
important condition of thinking. Logic has a perfect 
right to champion such conditions. It is not called 
upon to be a passive judge of consistency alone. 

The personal conditions of thought are also impor- 
tant. The prime condition is the recognition of a prob- 
lem. Back of this recognition lies the attitude which 
faces problems and even goes to meet them halfway. 
This attitude is partly temperamental, partly the con- 
sequence of training. On the practical side of life, so 
long as our habitual ways of acting are sufficient to 
meet the conditions which confront us, there is little 
reflective thought because there is little need for it. 
There is mental activity, of course, because we must 
constantly recognize and classify things and situations ; 
but this classificatory interpretation is usually so im- 
mediate that the individual does not need to pause, or, 
if he does pause, it is only for a moment. Difficulties 
arise, however, frequently enough, and the course of 
action is stayed. New adjustments must be worked 
out, and these adjustments depend upon the proper 
location of the difficulty and the discovery of its nature 
and remedy. Thinking intervenes at such a time. It 
is the sign and consequence of uncertainty, doubt, in- 
ability to interpret. How successfully the individual 
meets the problem depends upon his training, capacity, 
and character. 

The Setting of Thought. Thinking arises and 
takes its course in the mind of an individual endowed 
with a fund of past experiences. The problem which 
occasions thinking involves a conflict within experi- 



18 THE ESSENTIALS OF LOGIC 

ence and calls into play all that is in any way relevant. 
Familiar ideas, prejudices, habits, memories, all enter 
into the council-chamber and demand audience. Think- 
ing is the individual's experience in process of internal 
adjustment. 

We may say, then, that thinking is purposive and 
selective. It is an expression of the growth of the 
mind. But the mind is distorted by old beliefs and 
prejudices and is very frequently deflected from the 
truth. It is like a river whose banks throw the current 
from side to side and produce in it all sorts of treach- 
erous eddies. The logician must do the work of an 
engineer. He must point out the dangers which con- 
front the mind which desires to think truly. 

Why we think. Our study of the conditions and 
setting of thought enables us to answer the question, 
* Why do we think ? ' There is both a practical and a 
theoretical urgency behind thought. Life demands that 
problems be solved in order that we may act wisely. 
When our habits push us in , different directions, we 
must work out some suggestion which satisfies our mind 
or we are distraught. Besides, we know from past ex- 
perience how dangerous it is to trust to a chance idea. 
We want to have a fair degree of assurance of the con- 
sequences before we act. To think is to rehearse the 
course of events beforehand and to meet every emer- 
gency with its appropriate interpretation. 

But psychologists inform us that it is the very nature 
of the mind to work out harmonious ideas. The things 
we see are the products of adjustments. However far 
down we go in our. mental life, we find the endeavor 
to harmonize various elements with one another. " The 



THE NATURE AND SETTING OF THOUGHT 19 

sensations that are received are added to or changed to 
make them correspond more exactly to what from our 
different earlier experiences we know they must be. 
One always corrects the shape of the table-top as it 
appears in perspective. The angles are right angles as 
we see them, although the image must have acute and 
obtuse angles. One always makes an allowance for dis- 
tance in the size of an object that is seen. The same 
object is always given the same size no matter how far 
away it may be, while the image on the retina dimin- 
ishes constantly as the distance increases." 1 Thus, pro- 
cesses of adjustment are characteristic of the mental 
life at its different levels. This same tendency ex- 
presses itself in thinking. Thinking arises naturally 
and inevitably when the adjustment cannot be made 
almost automatically. 

We have stressed practical problems as an explana- 
tion of thought ; but theoretical problems are, at the 
present day, as fruitful in thought. These two types 
of problems are intimately interwoven by the very na- 
ture of life, for there are few ideas which do not have 
a bearing upon conduct. Yet the interests involved 
are fairly distinguishable. The growth of science has 
assisted man to develop interests of an impersonal 
kind, and about these interests and the investigations 
connected with them arise theoretical problems. Facts 
must be interpreted by theories and these theories 
must be harmonized so far as possible. The trained 
human mind is not satisfied with disorder and contra- 
diction ; it seeks to bring harmony out of chaos and to 
organize its ideas into a harmonious whole. Conflict in 

1 Pillsbury, Essentials of Psychology, p. 157. 



20 THE ESSENTIALS OF LOGIC 

any realm is to such a mind a stimulus to thought. The 
process of thinking has back of it all the forces and 
habits which demand order. To say that man is ra- 
tional is to say that he seeks adjustment among his 
ideas. 

Processes preliminary to Reflective Thought. 
The processes preliminary to reflective thought are, 
roughly speaking, two : perception and conception. We 
must have percepts and the ideas formed from them 
before we can think. Together, they furnish the ma- 
terial within which thinking goes on. It must not 
be supposed that percepts and concepts (ideas) are 
given apart from mental activity, but it is true to say 
that the higher mental processes, such as judging, ana- 
lyzing, drawing conclusions, and argumentation, occur 
within a field of experience already fairly stable and 
definite. We see the external world, recognize various 
familiar objects in it, know what to expect of them, 
and have a pretty generous fund of ideas when we are 
engaged in the solution of any particular problem. 
The individual's mind is constantly adding to its store 
of information and its working system of distinctions, 
classification, and expectations. It is correct, then, to 
say that thinking represents the growing point of the 
mind, and that it leaves a sediment, so to speak, of 
ideas and habits and points of view. We must remem- 
ber, however, that any part of this accepted knowledge 
may be challenged by new problems and new experi- 
ences ; hence we must think of the mind as a living 
organism rather than as a building in which one story 
is added to another. 

The psychologist has much to tell us of sensations, of 



THE NATURE AND SETTING OF THOUGHT 21 

their qualities and intensities and number. This infor- 
mation does not have much bearing upon the subject- 
matter of logic, interesting as it is in itself. We know 
that the sense organs must be stimulated before we can 
have these sensations with which, in the rough and un- 
analyzed, we are all of us familiar. The next level after 
sensation is perception. It is of advantage to the logi- 
cian to realize that perception is a complex process and 
that the percepts which we have as a result may be 
partly false. Whenever there is possibility of error, the 
logician cannot be indifferent. When we come to a 
study of scientific method, we shall have considerable to 
say about errors in observation. A few words about the 
general character of percepts and perception may not 
be amiss at this point. 

Put technically, percepts are the mental objects 
which result from the interpretation of sensory stimuli 
by centrally aroused processes. They are the primary 
mental objects of which we are aware when we use our 
senses. There is a sensory basis in all percepts ; but 
there is, furthermore, a large element of applied past 
experience. A percept is really a mental product to the 
making of which there has gone much trial, selection, 
and adjustment. The cumulative result of these proc- 
esses is given as an object, while the processes them- 
selves seldom appear in consciousness. So far as more 
is given in the percept than the senses warranty the 
logician speaks of the inferential element in percep- 
tion. It is because of this inferential element that per- 
ceptions may be erroneous. We may see things which 
are not present because we take a certain sensory cue 
and add to it qualities which often have accompanied it 



22 



THE ESSENTIALS OF LOGIC 



in our experience. What we shall unconsciously add de- 
pends largely upon the setting and upon the ideas which 
are occupying our minds. The following examples may 
make this possibility of error in perception more evident. 
In the following figure taken from Jastrow, one can 
actually see dim lines suggested by the heavy lines that 
are drawn. These are supplied by memory. 1 



EDITOR 



This second figure may be seen as a rabbit's head or 
as a duck's according to the thought which is upper- 
most. 2 




1 Jastrow, Fact and Fable in Psychology, Fig-. 2. 2 Ibid., Fig 1 . 19. 



THE NATURE AND SETTING OF THOUGHT 23 

These illusions as they are called, serve to bring out 
the amount of interpretation which is at work in every- 
day life. Here is another example : " If a sportsman, 
while shooting woodcock in cover, sees a bird about the 
size and color of a woodcock get up and fly through the 
foliage, not having time to see more than that it is a 
bird of such a size and color, he immediately supplies 
by inference the other qualities of a woodcock, and is 
afterwards disgusted to find that he has shot a thrush. 
I have done so myself, and could hardly believe that the 
thrush was the bird I had fired at, so complete was my 
mental supplement to my visual perception." x 

Speaking of such illusions, William James says: 
"Twenty times a day the lover, perambulating the 
streets with his preoccupied fancy, will think he per- 
ceives his idol's bonnet before him." 

Conception arises upon perception as a foundation. 
Concrete, perceived objects are dissected into elements, 
and these elements, loosened from their particular con- 
text, are capable of repeated recall. Concepts are men- 
tal objects which are (1) not directly connected with 
the stimulation of sense-organs, and (2) are under our 
control so far as our having or not having them is con- 
cerned. The mental processes which make concepts 
possible are analysis and abstraction assisted by the 
method of comparison. We note the likenesses and dif- 
ferences between things. Certain qualities begin to stand 
out and are selected by the attention. These quali- 

1 Romanes, Mental Evolution in Animals : , p. 324. 

2 The student will find James's discussions of illusions extremely in- 
teresting*, especially pages 95 to 103 of the second volume of the Prin- 
ciples of Psychology. MUnsterberg's On the Witness Stand, chap. I, is also 
suggestive. 



24 THE ESSENTIALS OF LOGIC 

ties and relations are then abstracted or considered by 
themselves, while the other features of the thing are 
disregarded. The result of this analysis is the isolation 
of the quality or relation from its context and our 
ability to recall it again and again at need. Such ab- 
stracted, repeatable mental objects are called 6 con- 
cepts.' Other terms, sometimes employed, are ' mean- 
ings,' ' ideas,' 4 universals.' This last term stands for a 
species of concept which is of special interest to the 
logician, and frequently used in philosophy. A universal 
is a concept which applies to an indefinite number of 
individual things. Any class name is a good example 
of a universal. We all have the idea of a horse, of an 
auto, of a soldier, etc. Such ideas are universals. 

The ability to form concepts is essential to reason- 
ing and reflective thought in general. Conceptual ele- 
ments, obtained by comparison and abstraction, are 
organized together in all sorts of ways. Only by means 
of concepts are we able to rise above the particular field 
of concrete perception spread out before our senses. 
Knowledge is primarily an affair of conception, of rules 
and principles, facts and theories. But it must not be 
forgotten that these elements work back into and con- 
trol our interpretation *of the world we see about us. 
There is a constant and responsible interplay of per- 
ception and conception in our minds. Logic concerns 
itself with this interplay so far as it can be made the 
object of a critical reflection. 

Fact and Theory. The distinction between percept 
and concept is more characteristic of psychology than 
of logic. For the latter, the more distinctive contrast is 
between fact and theory. In any argument, we con- 



THE NATURE AND SETTING OF THOUGHT 25 

stantly seek to separate what may be considered the 
facts of the case from the theory which is added to it as 
an interpretation. Argument and dispute arise where 
fact and theory are not clearly separated ; and the first 
step to the settlement of the argument is an agreement 
as to what is fact and what is theory. Now, fact is that 
which is admitted for the purpose of the argument ; it 
is that which is, temporarily at least, considered indis- 
putable. And it is interesting to note that fact in this 
sense may be either concrete or abstract. The Law of 
Gravitation is a fact because it is an assertion which I 
do not question. A theory, on the other hand, is that 
which is tentative and disputable. It needs support, 
proof, corroboration. 

The first step in reflective thought or argument is, 
therefore, to distinguish fact from theory, the indisputa- 
ble from the disputable. " In practice, assertions are 
seldom or never wholly untrue, especially when they 
correspond to a genuine belief. It is sometimes difficult, 
but seldom impossible (if it be thought worth while), to 
find a basis of agreement even with those whose view 
seems most opposed to our own. Some part of the way 
they go with us, and then the roads branch off. Why 
did they leave our road, or why did we leave theirs ? 
That question and its answer is the beginning of argu- 
ment. The matter of argument is always matter of 
opinion ; not fact but theory ; not fact but inference 
from fact." 1 

Knowledge a Growth. No problem or doubt which 
gives rise to reflective thought challenges all the indi- 
vidual's world. There is always fact as well as theory, 
1 Sidgwick, The Process of Argument, p. 18. 



26 THE ESSENTIALS OF LOGIC 

the accepted as well as the disputed. Knowledge is a 
growth and, like every growth, has a structure of its 
own. Logic has to pay considerable attention to the 
structure of knowledge and its medium, language. If 
argument is knowledge in the making, it would seem 
impossible to understand it apart from pretty adequate 
ideas of what knowledge as made consists in. All 
through logic, then, we see process and product, growth 
and achievement, dovetailed together. It is really im- 
possible to understand one apart from the other. All 
problems arise within the knowledge already attained 
and reflect its structure. This fact explains why logic 
has to take up so many topics which seem linguistic 
or concern themselves with the divisions, classifica- 
tions, and distinctions in knowledge rather than with 
discovery, argument, and reasoning. 

REFERENCES 

Bode, An Outline of Logic, chap. I. 

Bosanquet, The Essentials of Logic, Lecture II. 

Dewey, How We Think, chap. I. 

Pillsbury, Essentials of Psychology, chaps, vn and IX. 

James, Principles of Psychology, vol. n, chap. xxn. 



CHAPTER III 

ABOUT TERMS 

The Unit of Thought. The logician considers the 
judgment or the proposition as the unit of thought. 
The conclusion of a vital act of thought may find ex- 
pression in a proposition, but in nothing short of it. 
Thus, in answer to a friend's question, I may say that a 
certain man is reliable; but I cannot use the words 
4 man ' and ' reliable ' in isolation and convey any as- 
sured meaning. The unit of thought is a complex idea, 
which is asserted or denied. Since thinking arises under 
the stimulus of a problem, its result must be definite, 
it must assert or deny something. This definite solution 
of a problem is called a ' judgment ' and its verbal form 
a ' proposition.' 

The proposition can be analyzed into elements which 
are called ' terms.' These terms exhibit the complexity 
of the proposition, and are always present in a relation 
characteristic of the concrete act of thought. 'Fire 
burns,' 4 Justice is kingly,' are propositions in which 
there is both unity and complexity, or, better yet, unity 
in complexity. In trying to understand the judgment, 
we must carefully distinguish between the mental proc- 
ess of thinking which finds its goal in an accepted idea 
and the accepted idea itself. It is this latter which finds 
expression in the proposition and which is analyzed by 
the logician. 

The Elements of the Proposition. A proposition 
is always analyzable into a subject and a predicate. The 



28 THE ESSENTIALS OF LOGIC 

subject is that about which something is stated, while 
the predicate is that which is stated about the subject. 
These two elements are called the ' subject term ' and 
the ' predicate term ' respectively. And this brings us 
to the definition of a 'logical term.' It is any word or 
group of words which can serve as the subject or the 
predicate of a proposition. But these two terms do not 
exhaust the proposition. There is, further, the word 
which stands for the relation between these terms. This 
is called the ' copula.' In the proposition, ' Abraham 
Lincoln was a wise statesman,' the subject term con- 
sists of two words and is a proper name, the predicate 
term contains three words, while the copula is a form 
of the verb * to be.' 

Words and Terms. It should be noted that the 
different parts of speech are not equally capable of 
acting as terms or as the nucleus of terms. Nouns, pro- 
nouns, verbs, and adjectives have the character or func- 
tion which enables them to act as the essential part 
of a term or even as a term. Such words are called 
4 categorematic ' or asserting words. Other words are 
not able to designate an object of thought, but are sub- 
sidiary to such designation. They are called 4 syncate- 
gorematic' Adverbs, conjunctions, and prepositions 
are connective or qualifying words, and are therefore 
classed as syncategorematic. 

Since terms often consist of many words grouped to- 
gether, categorematic words may be found combined 
together by means of syncategorematic words. In the 
proposition, * Justice is kingly though no lung be just,' 
the words italicized are categorematic, while the others 
are syncategorematic. This distinction is, perhaps, more 



ABOUT TERMS 29 

grammatical than logical ; but it serves to stress the fact 
that a logical term is other than a word. 

Kinds of Terms. Terms fall into different classes 
according to the point of view that is dominant. The 
first division is into ' concrete ' and. ' abstract.' Concrete 
terms, again, are divided into singular or individual, 
general or class, and collective terms. Let us examine 
these divisions, which are the most important, before 
glancing at other kinds of terms. 

An abstract term is the name of a quality or rela- 
tion taken apart from its setting. In the study of con- 
ception, the nature of abstraction was referred to. To 
abstract is to draw off or take away. But an abstract 
term is not simply a word which calls up an idea which 
is conceptual in character, for all words do this, it is 
a word which signifies an attribute or relation taken 
apart from any individual object. It is the relation of 
the idea to realities which are thing-like which is disre- 
garded. Thus, ' sweetness ' is an abstract term because 
it signifies a conceptual object obtained by abstract- 
ing a quality of physical things and considering it by 
itself. The objects signified by abstract terms cannot 
possibly be perceived. 

Some abstract terms are farther from sense-percep- 
tion than are others. This is because the objects of which 
they are characteristics involve more construction. Thus, 
'equality,' ' animality,' 'constitutionality,' 'discipline,' 
are abstract terms at second remove, so to speak. It is 
to be noted that abstract terms are always nouns. 

A few words need to be said concerning the dangers 
involved in the use of abstract terms. Since they are 
nouns, they are readily thought of as referring to indi- 



30 THE ESSENTIALS OF LOGIC 

vidual things, more subtle than physical things, yet 
somehow real after the same fashion. The result is a 
fallacy which is usually called the ' fallacy of hyposta- 
tization.' Other writers speak of it as the ' fallacy of 
abstract terms.' It consists of treating abstractions as 
veritable things. " Our everyday use of such terms as 
4 conscience,' 6 memory,' and ' will ' shows further how 
ingrained is this habit of treating abstractions as though 
they were independent things. In reality these terms 
are the names of attributes. It is not uncommon, how- 
ever, to find that conscience, for example, is conceived, 
in a vague fashion, as though it were some kind of thing, 
inhabiting the inmost recesses of the soul and perform- 
ing the functions of an oracle. Similarly, there is no 
separate thing called memory or will, but only different 
instances of remembering and willing." 1 

In contrast to an abstract term, a concrete term is a 
word or group of words which refers to a person or 
a thing, or a group of persons or things. If there is 
any doubt whether a given term is abstract or concrete, 
the test to apply is, 4 What does it lead us to think of ? ' 
If it lead us to think about definite individuals, it is 
concrete ; if it lead us to think about attributes, it is 
abstract. Thus, ; man,' 4 animal,' c a society,' ' Lake 
Michigan,' ' a red apple ' are concrete terms ; fi hu- 
manity,' ' animality,' ' society,' ' redness ' are abstract. 

Concrete terms, we have said, are divisible into sin- 
gular, general, and collective. These terms agree in their 
function of calling to mind things ; they differ in the 
number of things implied and in the way they are taken. 

A singidar or individual term is one which applies 
1 Bode, An Outline of Logic, p. 49. 



ABOUT TERMS 31 

to only one thing. Such a term is selective and is used 
to identify, or direct our thoughts to a thing or expe- 
rience which is regarded as a distinct existence. Ex- 
amples : i the large dictionary in this room,' ' the center 
of the earth,' 6 the fifth page of this book.' 

It should be noted that the point of view determines 
in large measure what shall be regarded as a single 
thing. A note of music may awaken an interest which 
leads to a selective emphasis on it so that it stands out 
from its setting, or it may be completely merged in the 
whole composition. It is worth while to reflect upon this 
relativity of what we shall consider a thing to our inter- 
est We cut out things from continuous wholes much as 
the housewife cuts out cookies from the pastry. We 
divide up the world into larger or smaller parts in ac- 
cordance with what attracts our attention. A mountain is 
a thing, so is a boulder on its summit, so is a peculiarly 
colored portion of the boulder, so is, perhaps, a molecule 
in it, etc. A singular term helps the individual to carry 
on this process of selective analysis, and enables him to 
direct the thoughts of another person to the same goal. 

There are two methods for the formation of singular 
terms. The first method consists in the taking of a term 
which applies equally well to many things and adding 
new words until the application is obviously limited to 
one thing alone. The definite article always indicates 
the singular term. Very often the presence of the super- 
lative form of an adjective or adverb helps to carry out 
this process of narrowing the application of the term to 
one thing. Examples : 4 the greatest politician in the 
United States to-day,' ' the man who ran fastest in the 
meet.' The second method is to adopt a term arbitrarily 



32 THE ESSENTIALS OF LOGIC 

as a sign of a particular individual. Since language 
is social, a social element enters here. This use of the 
term must be consented to by the group. Personal 
names are of this character. Individuals are christened 
according to a socially recognized procedure. One is 
called ' Bernard Shaw ' ; another, ' William Smith ' ; 
another, ' If-Christ-had-not-died-you-would-have-been- 
damned Barebones.' It is interesting to note that a 
personal name is not always sufficient to select the one 
person meant. In that case, some descriptive word or 
words must be added. We all remember the ' Fiddler 
Smiths ' and ' Little John Petersens ' of our boyhood. 

A general term is one which applies to any number 
of things. General terms are names of kinds or classes. 
Grammar makes the distinction between common and 
proper nouns which corresponds to a difference of nu- 
merical application. Examples of general terms are, 
4 dog,' ' member of Congress,' ' citizens of the United 
States,' 'holidays.' 

The objects covered by a general term are members 
of a class. Such objects agree in certain characteris- 
tics and are classed together because of this agreement. 
These points of resemblance are called ' attributes ' of 
the class. It should be noted that all objects have some- 
thing in common, and that the number of possible classes 
is infinite. In both practical life and science, kinds or 
groups of objects having very much in common, are 
worked out and established as a matter of general knowl- 
edge. Such classes have accepted names. 4 Salts,' « halo- 
gens,' * acids,' ' vertebrates,' ' mollusks,' ' constitutional 
monarchies,' 4 fruits,' etc., are names of well-understood 
classes. 



ABOUT TERMS 33 

We shall have occasion to consider class names again 
when we come to the distinction between ' denotation ' 
and 'connotation.' We shall see that general terms have 
two functions ; they denote the individuals to which they 
apply and they connote the attributes which they imply. 

Collective terms are a special class of concrete terms. 
They arise from the ability the human mind has of 
grouping objects together and considering them in their 
collective aspect. A collective term is one which applies 
to a group of objects in which the individual members 
are lost sight of in the whole. Such terms may be 
either singular or general. Examples of singular collec- 
tives are, ' the American navy,' ' the crowd before the 
courthouse,' * the woman's club. ' * Navy,' ' family,' 
i tribe,' ' state,' 4 teacher's association,' are general col- 
lectives. 

When we are referring to some specific group, the 
term is employed as a singular. ' The American navy 
is fairly efficient.' ' This crowd of students is out for a 
good time/ A general collective is used as a general 
term on the ground that there are various groups with 
the same characteristics. It is used distributively of the 
particular groups covered and collectively of the mem- 
bers of any one group. < Excited mobs are dangerous.' 
4 Woman's clubs are becoming social centers.' This dis- 
tinction will become clearer when we take up ' conno- 
tation ' and 4 denotation.' It is necessary to go beyond 
the mere form of the words to what is thought of in 
order to distinguish between singular and general col- 
lectives. 

Ambiguity sometimes arises from the fact that the 
English word * all ' is used both distributively and col- 



34 THE ESSENTIALS OF LOGIC 

lectively. " That is, it may mean ' all taken together p 
or ' each and every.' Thus, we can say : ' All the angles 
of a triangle are less than two right angles,' and * All 
the angles of a triangle are equal to two right angles.' 
In the former sentence, the word * all ' is used distribu- 
tively, in the latter collectively. In Latin two different 
words are used : cuncti expresses the collective sense of 
4 all,' and omnes its distributive signification." 1 

Other Kinds of Terms. We have defined and ex- 
amined abstract, concrete, singular, general, and collec- 
tive terms. But terms are divided from other points of 
view into ' absolute ' and ' relative,' and into ' positive,' 
4 negative,' and 4 privative' terms. These distinctions 
are significant enough to justify some consideration. 

An absolute term is one which refers to an object 
or quality considered by itself. The supposition is that 
such an object of thought has meaning in its own right ; 
it does not depend on its relation to something else for 
an essential part of its meaning. Thus, 4 stone,' 4 build- 
ing,' ' the State of Michigan ' are absolute terms. A 
relative term is one which derives an essential part of 
its meaning from its relation to something else. Ex- 
amples of relative terms are, ' shepherd,' 4 patient,' 
6 ruler,' ' citizen,' 4 pupil.' Relative terms usually go in 
pairs which imply one another and are then called 4 cor- 
relatives.' Thus, 4 teacher ' implies 4 pupils ' and 4 par- 
ent ' implies 4 child ' ; and the reverse is also the case. 

It is sometimes said that all things are relative in the 
sense that they are interdependent. This is true, yet it 
does not invalidate the logical distinction we have just 
discussed. At the level of common sense, we usually 

1 Creighton, An Introductory Logic, p. 51. 



ABOUT TERMS 35 

ignore the relations which bind things to one another 
because they do not come out in perception. Only when 
relations stand out so clearly that they cannot be dis- 
regarded, do they form an essential part of our thought. 
Man is absolute, but a man as a teacher is relative. 
This term stresses a relation into which a man may 
enter. 

But the term ' relative ' is sometimes used in another 
sense. A word may involve a standard. 'Goodness,' 
4 badness,' ' luxury,' ' poverty,' 6 beautiful,' and 6 slow- 
ness ' are examples of relatives of this kind. The danger 
lies in the fact that the standard is variable from per- 
son to person, from class to class in society, and from 
period to period in history. This variability, when not 
recognized, is a fruitful source of confusion. " To rec- 
ognize and point out this character of relativity may 
on occasion serve to forestall much fruitless argument. 
For example, the question may be asked, 'Are the 
people of the present day more moral than those of the 
past ? ' Before we undertake to express an opinion we 
should ascertain what is meant by ' more moral.' To 
judge the past by present-day standards is one thing : 
to judge it by its own standards is quite another. Again, 
the question may be raised whether or not students who 
go into business are, as a rule, more capable than those 
who adopt the profession of teaching. Discussions of a 
question like this are prone to overlook the relativity of 
a phrase like ' more capable.' Until we specify whether 
we mean ' capable for business ' or ' capable for teach- 
ing' or some other form of capableness, argument is 
likely to be futile." x The teacher in social ethics is 

1 Bode, An Outline of Logic, p. 46. 



36 THE ESSENTIALS OF LOGIC 

bound to meet questions which turn around the estab- 
lishment of &fair standard for such things as expendi- 
ture. And this term ; fair ' is itself obviously a relative 
term. 

The distinction between positive and negative terms is 
obvious enough. A positive term is one which implies 
the presence of a quality or qualities. Thus, 4 efficient,' 
4 selfish,' 4 happy,' and 4 heavy' are positive terms. A 
negative term is one which implies the absence of 
such qualities. 4 Inefficiency,' « disloyal,' 4 unselfish ' 
are negative terms. In the English language, such pre- 
fixes and suffixes as 4 un,' 4 in,' 4 dis,' * a,' and 4 less ' are 
used to form negative from positive terms. It should be 
noted that contrast-pairs formed in this way do not box 
the compass. Take, for example, the terms 4 patient ' 
and 4 impatient ' ; a man may not be exactly patient 
while he is still far from impatient. The logician must 
call attention to this fact, however trivial it may seem, 
because words shift their meanings. When we come to 
study the possible manipulations of a proposition, such 
as obversion, we shall see why it is necessary to deter- 
mine the exact opposite of a term. 4 Intemperate ' is not 
the contradictory of 4 temperate.' A little reflection and 
some care in the use of words are all that is needed. 
Attention should be called to another point. Too much 
stress should not be laid upon the mere form of words. 
It is always best to penetrate to the meaning. Thus, 
such terms as 4 invaluable ' and 4 unloosed ' are positive 
in their meaning, while it seems nonsense to speak of 
4 intemperance ' as negative. The absence of one quality 
means the presence of a condition just as positive. The 
negative form is an accident of language in such cases. 



ABOUT TERMS 37 

For the sake of completeness, we referred to the class 
of privative terms. A privative term is one which sig- 
nifies the absence of a quality which is usually present. 
Because of the importance of this lack to which they 
refer, they are positive in form. Examples : ' maimed,' 
4 deaf,' ' blind,' ' orphaned.' 

Connotation and Denotation. General or class 
terms have two functions : they apply to the members 
of the class and they serve to recall the common attri- 
butes of the class. Thus the term does double duty : it 
enables us to bear individual things in mind while 
thinking of them as belonging to a class, and it is a sign 
of the essential attributes of the class. 

This double function of class terms reflects the way 
in which such terms develop. We notice that certain 
things have points of similarity, and, if these common 
qualities are important to us, we group these things to- 
gether and think of them largely in terms of their com- 
mon qualities. As a matter of fact, we never think of 
the things without some thought of the qualities, nor of 
the qualities without the implicit assumption that they 
are possessed by things. We may say, then, that deno- 
tation and connotation go together just as inevitably as 
do qualities and things. They are the reflection into the 
class term of this natural and constant distinction. It 
is for this reason that general terms denote things and 
connote qualities. 

Synonyms for Connotation and Denotation. 
Instead of 'denotation,' some logicians speak of the ' ex- 
tension ' or * scope ' of the term. The corresponding 
names for ' connotation ' are ' intension ' and 6 compre- 
hension.' ' Denotation ' and ' connotation ' are prefer- 



38 THE ESSENTIALS OF LOGIC 

able because they have the verb forms, ' denote and 
' connote,' and the adjective forms, 4 denotative ' and 
' connotative.' 

The Inverse Variation of Connotation and De- 
notation. The wider or higher the class, the fewer the 
attributes which the members of the class have in com- 
mon. As you pass from a species to a genus in biology, 
the number of animals or plants covered by the term 
increases while the common attributes decrease in num- 
ber. This double fact is summarized by saying that de- 
notation and connotation vary inversely. This variation 
does not, however, follow any mathematical law. In- 
crease the number of qualities possessed in common, 
that is, widen the connotation, and the members of the 
class possessing these qualities will be fewer in number. 
The following series will illustrate this principle : 'man,' 
4 Americans,' 4 Americans of European descent,' 'native- 
born Americans,' ' native-born Americans who are citi- 
zens of Michigan,' etc. 

It should be noted that, in our actual thinking, the 
connotation of a term is more apt to be explicit than 
the denotation. We do not actually run over the various 
members of the class, but, instead, have some individual 
vaguely in mind as a specimen. 

Terms and Meaning. All words have meaning. 
This meaning varies from the most substantive and 
definite to the most fugitive and fluctuating. The mean- 
ing of a word is inseparable from the context in which 
it is used. It is for this reason that both the logician 
and the psychologist hold that the sentence or even the 
paragraph is the lowest unit of thought. A word or a 
group of words constitutes a term, and this term has a 



ABOUT TERMS 39 

complex meaning. It is, however, best to distinguish be- 
tween the meaning of a term and connotation. In the 
first place, the distinction between denotation and conno- 
tation comes out clearly only for class terms; in the second 
place, the meaning of a class term includes both its de- 
notation and its connotation. We mean the objects we 
think of as well as the qualities they have in common. 

REFERENCES 

Bode, An Outline of Logic, chap. IV. 
Creighton, An Introductory Logic, chap. iv. 
Joseph, An Introduction to Logic, chap. II. 
Schiller, Formal Logic, chap. u. 



CHAPTER IV 

THE USE AND MISUSE OF LANGUAGE 

The Necessity for Language. Logic deals with 
thinking and with knowledge which is the resultant of 
thinking. But thought is impossible without language. 
It is for this reason that logic has to concern itself so 
fully with language and its relation to thought. " Lan- 
guage is not merely an accompaniment of ideational 
activity ; it is an instrument essential to its develop- 
ment. It is an appropriate means of fixing attention 
upon ideally represented objects as distinguished from 
percepts. It becomes the more necessary the more ab- 
stract ideal representation is, — in other words, the less 
it contains of the concrete details of actual sense-per- 
ception. . . . Within the mind of the individual thinker 
it serves to fix attention on the object of his own ideas ; 
in communication with others, it serves to fix the atten- 
tion of the hearer on the ideally represented objects 
present to the mind of the speaker." * As we advance 
in our study of logic, we shall realize, ever more clearly, 
what an intimate part language plays. Systematic 
knowledge is bound up with the use of a definite set 
of symbols, though these symbols may be of various 
kinds. Each special science works out its own technical 
terms, while mathematics has advanced step by step 
with its notation. 

Language and Analysis. In a preceding chapter 2 

1 Stout, Manual of Psychology, p. 462. 

2 Chapter n, " The Nature and Setting of Thought." 



THE USE AND MISUSE OF LANGUAGE 41 

we suggested that reasoning is based upon the percep- 
tion of likeness and difference. Now, language assists 
such discrimination by giving names to the common 
factors and aiding in their recall and free manipulation 
apart from perception. Gradually a world of ideas is 
built up in which man may freely move. Words are 
the means by which such ideas are fixated. It has been 
proved by experiment that we both observe and remem- 
ber features of our experience better if we possess 
words to attach to them. 

The Logical Law of Language. The logical law 
of language is non-ambiguity. Actually, words are in- 
definite and misty on their edges. We use them in a 
rough-and-ready fashion. We feel their appropriateness 
and develop habits in their use. The consequence is 
that there is not enough delicacy in discrimination ; we 
tend to class things together when we notice that they 
have common features. Yet the differences may be of 
more significance for the problem in hand than the 
similarities. 

The neglect of relevant distinctions, when these are 
important for clear thinking or adequate statement, is 
ambiguity. The ideal of the logician is to encourage 
individuals in those mental habits of accuracy and dis- 
crimination which are calculated to prevent ambiguity. 
The logical law of language is non-ambiguity, an ideal 
to which we should approach ever more nearly. 

Causes of Ambiguity. There are many causes of 
ambiguity, but the basic cause is mental. Ideas are 
allowed to remain vague, and, as a consequence, they 
overlap and get into one another's way. Just as things 
are often classed roughly together because their differ- 



42 THE ESSENTIALS OF LOGIC 

ences are not noted, so ideas are only too frequently 
merged and confused. But clear and accurate thinking 
depends as much upon the awareness of differences as 
upon the awareness of similarities. Only he who is 
willing to take the trouble to distinguish things and 
ideas which are ordinarily grouped roughly together, 
can escape the pitfall of ambiguity. 

But ambiguity has a social significance. Incorrect 
and inadequate thinking when expressed in language 
appears as ambiguous statements and arguments. Such 
statements are apt to deceive the unwary because they 
also refuse to make an analysis of the ideas involved. 
Hence ambiguities tend to propagate themselves and 
father a series of fallacies. 

Now, while unwillingness or inability to analyze the 
various fields of experience, in order to build up clear- 
cut ideas not easily confused, is the basic cause of ambi- 
guity, there are other causes at work, the variation of 
the meaning of words with the purpose or general con- 
text, and the imperfections of language as an instru- 
ment. It is difficult for language to keep pace with the 
subtlety and flexibility of thought. It is so easy to sub- 
stitute the average meaning for the particular meaning 
which the situation demands. Again, a word may have, 
and usually does have, more than one meaning of an 
average sort ; and, to make matters worse, words are 
constantly changing their meanings. We always have 
more ideas than words with which to express them. It 
may be said that this ability of a single word to do duty 
for more than one idea is a perfection rather than an 
imperfection, but it certainly brings its dangers. A 
sharp eye for the context or purpose is the main safe- 



THE USE AND MISUSE OF LANGUAGE 43 

guard. If this is not obvious to the reader or listener, 
ambiguity is unavoidable. 

Univocal Words. Words which have only one 
meaning are called ' univocal.' The best examples of 
univocal words are to be found in the technical terms 
of the special sciences. In these, a term is adopted, or 
made, as an accepted sign of a definite idea reached by 
painstaking investigation. Consequently, the danger of 
ambiguity is at a minimum. To secure such carefully 
delimited ideas is one of the chief purposes of any sci- 
ence ; it is a recognized condition of advance. The 
technical terms of a special science when taken together 
form its nomenclature. Thus, ' molecule,' i electron,' 
' vertebrate,' ' cell,' ' angle ' are technical terms. It 
should, however, be noted that not all technical terms 
are strictly univocal ; it is only when they are given in 
the context of their special field that they have but one 
meaning. But this context is easily recognized. 

Equivocal Words. Words which have more than 
one meaning are 'equivocal.' The vast majority of 
words which do not apply to material things are equiv- 
ocal, as can be seen by glancing over the columns of 
any large dictionary. Thus, to take a simple word like 
4 stop,' we find that it means (1) 'to close,' (2) 'to 
confine,' (3) ' to arrest,' (4) ' to interrupt.' Besides 
these popular uses, it has technical meanings in music, 
rhetoric, optics, horticulture, and finance. It is no won- 
der that a foreigner has difficulty in learning another 
language, and I am sure that, if all the humorous 
stories told in this connection are not true, at least 
there is ground for most of them. The truth is that 
there are not enough words to go around, and we are 



44 THE ESSENTIALS OF LOGIC 

obliged to make one word do the duty of many. A per- 
ception of the setting is essential if ambiguity is to be 
avoided. The only practical advice the logician can 
offer is to seek for the particular meaning and not trust 
the average or general meaning of the term. 

"Words change their Meanings. There are several 
tendencies at work to change the meanings of words. 
The three most important are generalization, specializa- 
tion, and transfer of meaning by association and analogy. 

At first, a word is the sign of a concrete thing or 
class of things. It is later extended to all those things 
which have a conspicuous attribute in common. As time 
goes on, extensions to more abstract objects take place. 
This change of application from a concrete particular 
to analogous things and objects of thought is called 
4 generalization.' " The word 6 law ' has undergone ex- 
pansion under the pressure of physical research. Reg- 
ularity, uniformity, constancy of occurrence is a much 
wider idea than bare authoritative prescription enforc- 
ing obedience under the threat of punishment — which 
is the simple juridical conception." * How easily ambi- 
guity arises when two meanings coexist can be seen 
from the following quotation: "The existence of a 
power is even implied in the phrase ' laws of nature,' 
constantly used by science ; for wherever there is a law 
there must be a lawgiver, and the lawgiver must be 
presumed capable of suspending the operation of law." 2 
Another instance of this ambiguity of the word law 
has come to light in recent discussions bearing upon 
the nature of 'international law.' The English word 

1 Davidson, The Logic of Definition, p. 5. 

2 Gold win Smith, Guesses at the Riddle of Existence, p. 143. 



THE USE AND MISUSE OF LANGUAGE 45 

4 law ' translates what is expressed in continental tongues 
by two words ; in German by recht and gesetz, in French 
by droit and loi. Is there an international law ? If we 
mean by 'law,' gesetz and loi, no ; if we mean recht and 
droit, yes. It is obvious that we have too few words in 
such a case. 

Other simpler examples of this principle of general- 
ization are « fluid,' 4 acid,' 4 curve,' and 4 oval.' We pass 
from the particular to the more general and abstract. 

Again, words may take on a more special meaning. 
4 Priest,' 4 minister,' 4 captain,' 4 clerk ' are examples of 
this tendency to select a special application of the more 
general meaning and to ignore the other meanings. One 
of the most interesting cases of this specialization which 
has led to ambiguity is the word ' prove.' Originally it 
meant 4 to test ' as in the saying, " The exception proves 
the rule." Now it means * to test successfully.' I pre- 
sume that many a one has wondered how the exception 
could prove the rule. 

There is, finally, the tendency to transfer a word to 
analogous or associated objects. Thus, the word 4 church* 
is used to designate the religious body, the building, and 
some temporary group of worshipers. We speak of the 
4 chair ' when w r e mean the presiding officer, or of the 
4 bench ' when we mean the judiciary. It would be 
right to list under this heading those epithets which are 
based on felt analogies. Such epithets startle the mind 
and force it to recognize similarities which would other- 
wise have passed unnoticed. It is the poet, with his 
keen sensing of likenesses and differences, who is most 
apt to bring far-removed aspects of experience together 
by an illuminating phrase. We feel the appropriateness 



46 THE ESSENTIALS OF LOGIC 

of the expression while we hesitate to analyze it, so 
subtle and elusive is the connection. 

These classes of changes in the meanings of words 
make us realize what a complex instrument language is. 
It is necessary to know all the essential meanings of 
commonly used words and to have some idea of how 
new shades of significance are added. 

Vagueness. Vagueness is often the cause of ambi- 
guity, but it is not the same as ambiguity. Our ideas 
of the meanings of the words we use may be hazy, but, 
so long as the subject we are talking or thinking about 
is simple, this lack of definiteness in our ideas may not 
lead us astray. So long as the problem is general and 
relatively practical, no great measure of analysis is 
needed. We must remember that words are frequently 
used just to indicate things and to suggest plans of ac- 
tion and desirable attitudes. Thus, common nouns are 
seldom used incorrectly even though the majority of 
people would be hard put to it to give an exact defini- 
tion. Yet, even here, there is doubt when those excep- 
tional cases are met which fall on the dividing-line be- 
tween two classes. Is this man a doctor or a quack? Is 
this lawyer a genuine lawyer or a pettifogger? The 
trouble is, of course, not so much one of language as of 
classification. Classes shade into one another and their 
edges are blurred. Accuracy and completeness of classi- 
fication are the pre-conditions of clear ideas. 

The reason for vagueness in the understanding and 
application of words can partly be traced to the method 
by means of which the individual's vocabulary is devel- 
oped. Words are picked up in their special applications 
and then extended to what are judged to be similar 



THE USE AND MISUSE OF LANGUAGE 47 

cases. " The mode in which words are learned and ex- 
tended may be studied most simply in the nursery. A 
child, say, has learnt to say ' mambro ' when it sees its 
nurse. The nurse works a hand-turned sewing machine, 
and sings to it as she works. In the street the child 
sees an organ-grinder singing as he turns his handle : 
it calls ' mambro ' ; the nurse catches the meaning and 
the child is overjoyed. The organ-grinder has a mon- 
key: the child has an India-rubber monkey toy: it calls 
this also ' mambro.' " 1 The individual's vocabulary is 
built up under social control only of a rough-and-ready 
sort. It is adequate for general purposes, but not where 
accuracy is needed or where slight distinctions are very 
important. Where the demands are more exacting, 
vagueness is treacherous and leads to ambiguity. 

Abstract Terms particularly subject to Vague- 
ness. Where there is no chance to appeal to perception 
as a test for the meaning of a term, vagueness is almost 
certain to exist. We can pick up the word just as the 
child does, but it is another thing to reproduce the idea. 
That requires mental activity of a high degree. The 
logician stresses the fact that concepts are primary and 
words secondary. What is meant by such terms as 
4 happiness,' ' liberty,' ' social justice ' ? I who have 
spent years in analyzing their meanings feel that I have 
a right to be skeptical of some glib use of the terms. 
" When we come to words of which the logical concept 
is a complex relation, an obscure or intangible attribute, 
the defects of the popular conception and its tendencies 
to change and confusion are of the greatest practical im- 
portance. Take such words as ' Monarchy,' * tyranny/ 
1 Minto, Logic, Inductive and Deductive, p. 83. 



48 THE ESSENTIALS OF LOGIC 

'civil freedom,' 'freedom of contract,' 'landlord,' 'gen- 
tleman,' 'prig,' 'culture,' 'education,' 'temperance/ 
' generosity.' Not merely should we find it difficult to 
give an analytic definition of such words : we might 
be unable to do so, and yet flatter ourselves that we 
had a clear understanding of their meaning. But let 
two men begin to discuss any proposition in which 
any such word is involved and it will soon be found that 
they take the word in different senses." 1 Such terms 
are really technical and should be treated as such. The 
difficulty is, however, practical as well as scientific. Peo- 
ple are obliged to think about such subjects because 
of their duties and needs as citizens, and because such 
terms are frequent causes of dispute. What the logician 
must warn against is dogmatism. The average man is 
not easily persuaded that familiarity with a word does 
not involve knowledge of what it means. Such dogma- 
tism is one of the chief causes of error. 

Logic and Language. Logic deals with thought, 
but we can get at thought only through language. Now, 
language is not a transparent medium ; it veils as well 
as expresses the ideas and purposes which seek utter- 
ance and the understanding of other minds. The logi- 
cian must, therefore, be equal to the emergency of in- 
terpretation if sufficient clues are given. " The practicing 
logician, ever seeking behind the accidental parlance 
the necessary sequence of idea, studies the idiomatic ex- 
pression of thought, with which, however, and not with 
the expression, his concern truly lies." 2 

1 Minto, Logic, Inductive and Deductive, p. 86. 

2 Macleane, Reason, Thought, and Language, p. 9. 



THE USE AND MISUSE OF LANGUAGE 49 

REFERENCES 

Bode, An Outline of Logic, chap. in. 
James, Principles of Psychology, vol. li, chap. xxii. 
Jones, Logic, Inductive and Deductive, chap. iv. 
Macleane, Reason, Thought, and Language, Introduction. 
Minto, Logic, Inductive and Deductive, part 11, chap. I. 
Stout, Manual of Psychology, bk. iv, chap. v. 



CHAPTER V 

CLASSIFICATION AND DIVISION 

Classification and Classes. In our study of terms 
we distinguished class, or general, terms from the other 
kinds of terms. It is our present purpose to study in 
more detail the nature of classes and the character of 
the processes by which they are obtained. We shall see 
that the establishment of classes involves a large meas- 
ure of mental activity. Certain classes suggest them- 
selves quite naturally, while others are formed only after 
a deal of effort has been expended in the discovery of 
hidden relationships between things apparently different 
in nature. At whatever level classes are formed, com- 
parison, discrimination, analysis, and construction are 
at work, though with different intensities. It must never 
be forgotten that an object is not a member of a class 
in its own right, but because a class has been conceived 
by the human mind. Man and nature collaborate in 
the construction of classes. When a class has been es- 
tablished, however, its membership is potentially deter- 
mined by that very fact. Having conceived of verte- 
brates as a class, we cannot refuse membership to this 
or that creature because of our dislike for its bad habits 
or its ugly appearance. The Gila monster is as good 
a vertebrate as the most docile pussy that ever slept in 
her mistress's lap. 

We may define classification as the process of group- 
ing things together according to their possession of cer- 



CLASSIFICATION AND DIVISION 51 

tain selected common attributes. The things possessing 
these attributes are the members of the class, while the 
class is the members taken together. Such classes may be 
relatively permanent or quite temporary and occasional. 
The following quotation will illustrate the wide range 
of classes which the logician recognizes : " By a class 
will here be meant any imagined group of individual 
cases, whether real or unreal — a group in which every 
individual is supposed to resemble all the others in some 
respects, though differing in others. There are classes 
of actions and events just as of everything else ; 'mir- 
acle' is a class name, for instance; or 'coronation,' 
*l>attle,' 4 eclipse ' ; in fact any name which is used so 
as t0 admit of a plural — either simply, as ' miracles,' 
4 kggroes,' 4 battles,' or in the more circuitous form of 
4 pieces of gold,' 4 cases of deceit,' and so on." l There 
are filmy classes as well as the more ponderous classes 
of science. Both have their place for the mind of the 
logician. 

The Need for Classification. The world man is 
confronted with is very complex. It consists of objects 
and events of every conceivable kind. Moreover, this com- 
plex of things, actions, and events does not come ready- 
labeled. The world is not like a museum in which things 
of a kind are put together for our convenience. Instead, 
they are scattered about in space and time, and we 
must be ready to identify them wherever they are found. 
But identification involves mental activity. What is the 
character of this mental activity and why is it aroused ? 

The simplest form of identification is recognition. 
Psychologists inform us that recognition is often imme- 
1 Sidgwick, The Use of Words in Beasoning, p. 150. 



52 THE ESSENTIALS OP LOGIC 

diate, that an object arouses associates, and these give 
the sense of familiarity. " Part of the recognition of an 
object that is not handled or that does not give rise 
directly to movements is due to the fact that its uses 
are appreciated, that, when it is recognized, one knows 
at once what to do with it and how to use it." * Such 
immediate recognition is an unconscious classification. 
The character of the object is appreciated and the 
proper habits and attitude are aroused. Thus there is a 
practical aspect for identification. Similar things have 
similar properties : fire burns ; this kind of tree bears 
delicious fruit ; a silent baby is usually in mischief, 
etc. If we had to deal separately with each thing, 
we should not know what to do ; it would be impossible 
to bring past experience to bear. We may say, then, that 
classification, unconscious or conscious, is the only way 
in which we can handle our complex world of individual 
things. 

Types of Classification. But a felt identification 
is not sufficient for human needs. To handle things 
properly and commodiously mankind has had to work 
out methods and principles of grouping adapted to the 
purpose in hand. There are two main types of classifi- 
cation, the artificial and the natural, and these corre- 
spond to the dominant purpose. In an artificial classifi- 
cation, the purpose is to enable us to handle the facts 
in a given realm as quickly and easily as possible ; that 
is, the purpose is practical. In a natural classification, 
the purpose is to allow things or facts to arrange them- 
selves in accordance with their essential nature. Let 
us look a little more closely at these two types. 

1 Pillsbury, Essentials of Psychology, p. 209. 



CLASSIFICATION AND DIVISION 53 

Artificial Classification. In artificial classifications 
where the purpose is facility in handling, some obvious 
and, as a rule, external attribute is selected as the basis. 
A good example of this type is the method by which 
books are catalogued in a library. The first letter of the 
author's name determines the place of the book on the 
shelves and in the catalogue. If this simple device is 
insufficient, the subjects are likewise arranged alpha- 
betically. This mode of artificial classification is usually 
called 4 index classification.' 

Another kind of artificial classification is the so-called 
* diagnostic classification.' The purpose at work here is 
the identification of an object. A doctor wishes to diag- 
nose a disease so that he may know what procedure to 
adopt in his treatment of it ; or a collector wishes to 
label a butterfly which he has found. In both cases the 
the search is made for characteristics which will indi- 
cate the group to which the object belongs. Nature- 
study books are full of devices for identification of plants 
and animals according to pretty obvious traits. 

Natural Classifications. Natural classifications are, 
as we have said, based upon as thorough investigation 
of the nature of the things classified as is attainable 
at the time. The purpose is to find some arrangement 
which corresponds to our knowledge and reflects a 
kinship in the things themselves. Such an arrangement 
is a difficult feat to achieve, and the growth of science 
is traceable in the perfecting of systems of classi- 
fication. It is practically always necessary to pene- 
trate below the surface and to build on those underly- 
ing attributes which reveal themselves only to the eye 
of the trained observer. "Thus the classification of 



54 THE ESSENTIALS OF LOGIC 

birds, for instance, is based largely upon fundamental 
differences in anatomical structure. Birds, not as we 
see them, but as they are when stripped of plumage and 
in their nakedness, are the real objects of consideration 
in such a system of classification. The result is that in 
the same group there will appear side by side a number 
of birds whose surface markings are exceedingly dispar- 
ate, such as the blue jay and the crow, or the English 
sparrow and the cardinal. It is always a broadening 
experience, as regards our habits of thinking, when we 
are able to discover some essential similarity at the 
basis of a marked surface dissimilarity." 1 

Natural classification is scientific classification and 
reflects all the purposes and methods of science. The 
ultimate aim is, of course, explanation, but there is also 
the subordinate aim of convenience. This combination 
of purposes is very well brought out by Jevons : " By 
the classification of any series of objects is meant the 
actual or ideal arrangement together of those things 
which are like and the separation of those which are un- 
like, the purpose of the arrangement being, primarily, 
to disclose the correlations or laws of union of properties 
and circumstances, and secondarily, to facilitate the oper- 
ations of the mind in clearly conceiving and retaining 
in memory the characters of the objects in question." 

Natural Classification in the Light of Evolu- 
tion. During the eighteenth and the first half of the nine- 
teenth century, scientists believed in the existence of 
natural kinds of species which were changeless in char- 
acter and sharply distinct from one another. The task 
of the anatomist was to dissect these species and deter- 

1 Hibben, Logic, Deductive and Inductive, p. 58. 



CLASSIFICATION AND DIVISION 55 

mine their essential or defining marks. The hope was 
to enumerate and describe these fixed species once for 
all, and ' then to erect a scheme of classification into 
which they would all fit. But continued investiga- 
tion convinced naturalists that there was something 
scholastic and unreal in sharp distinctions ; that spe- 
cies merged with one another on the edges. With 
the gradual rise of the theory of evolution it came to 
be recognized that there are genetic relationships run- 
ning all through the organic realm and that species are, 
so to speak, abstractions which over-simplify nature. 
Species are not immutable, but, instead, shade over into 
one another. Classification is a tool which must not be 
read into the complex realm of things too naively. 

Character of Systematic Classification. Partic- 
ular classes are formed by grouping objects together 
according to their likenesses and differences. But a 
further task ensues, that of showing the relations be- 
tween the classes thus formed. We are not satisfied to 
leave particular classes in isolation, but demand a sys- 
tem of classification in which classes are arranged in 
accordance with conceived relations of coordination, 
subordination, and superordination. Such systems 
must express an internal unity which is manifested in 
various ways in the subordinate classes. All the classes 
must have certain attributes in common, and these com- 
mon attributes must not contradict the more specific 
attributes which differentiate the subordinate classes 
from one another. To put the matter less technically : 
classification works within some field of objects and 
seeks to arrange them by selecting, first, those attri- 
butes which they all possess, and, secondly, those groups 



56 



THE ESSENTIALS OF LOGIC 



of further and more specific attributes which divide the 
whole field into related yet distinct classes. So far as 
possible the differences which divide the whole into 
parts must be seen in their relation to the fundamental 
similarities. A particular class is a species (difference) 
of (similarity) the genus. A good classification should 
make it possible to see any fact in the light of the 
whole. The following example brings out this presence 
of an underlying agreement manifesting itself in differ- 
ent ways: 1 — 

Vegetable Kingdom 



Rootless, leaf- 
less, stemless 

plants 
(Thallophyta) 

I 

I 1 



Moss-like 

plants 
(Bryophyta) 



Fern-like 

plants 
(Pteridophyta) 



3 






& 

^ 



02 /— s 

B § 



Pn 



* 8. 



CO i*» 
co «g 

351 






Seed-bearing 

plants 
(Spermaphyta) 



Wkj 3 



CO o 

eo c 

1*8 

S3 O 



O^ 



T3 

0) 

■si 



co *> 

" &• 

o 
8 



o 

CD 

0) 
CO 

a 

a 






The student should examine the type of classifica- 
tion found in any good textbook in biology in order to 
familiarize himself with the mechanism of the process. 

Classification and Division. There is a very close 
connection between classification and another logical 
process called 'division.' The main difference in the 
meaning of the two terms is this : that when we classify, 
we think of ourselves as moving upward from the indi- 
1 Quoted from Taylor, Elpmentqry Logic, p. 45. 



CLASSIFICATION AND DIVISION 57 

vidual things to schemes of arrangement according to 
likeness and difference ; that when we divide, we think 
of ourselves as moving downward from the more gen- 
eral and inclusive modes of grouping to more specific 
sub-classes. Such a distinction is, however, rather arti- 
ficial, for, in the solution of any real problem of ar- 
rangement, our thought moves in both directions at 
once. Yet, while recognizing to the full this double 
movement of thought, it still remains true that logical 
division is a method with a definitely conceived form 
which can be used as a test of any classification. As a 
method, it is inclined to be more doctrinaire and a 
priori than classification. 

Technical Terms used in Division. Division is a 
process which may be carried through many stages. 
The general class with which it starts is called the 
4 summum genus/ that is, the highest genus. The sub- 
class with which it stops is called the 6 infimae species,' 
that is, the lowest species. Between these two extremes, 
the terms 4 species ' and ' genus ' are used as purely 
relative terms. In any series, the class above is the 
genus of the class below which is its species. The class 
directly above is the 'proximum genus' of the species 
just below. Where more than one species have the 
same proximum genus they are called ' coordinate spe- 
cies.' The coordinate species of a genus are called its 
'constituent species.' The principle used in dividing 
is called the ' f undamentum divisionis,' or basis of di- 
vision. It is that aspect of the summum genus which 
enables us to separate its constituent species. The dif- 
ferentia of a species is that characteristic which distin- 
guishes it from its coordinate species. 



58 THE ESSENTIALS OF LOGIC 

Rules of Division. To be valid, a logical division 
must observe the following rules : — 

1. A division must be complete. A complete division 
is one which exhausts the constituent species of the 
main class. 

The necessity for this rule is at once apparent. The 
neglect of any species may easily lead to confusion in 
both theory and practice. 

2. The constituent species into which the genus is 
divided must not overlap. A division is imperfect if an 
individual may belong to two species at the same time. 

A few words in regard to these rules may be advisa- 
ble. An incomplete division may be due to ignorance, 
lack of persistence, or to the special difficulties of the 
field. When the last is the case, it is sometimes met by 
forming a miscellaneous class to include obscure data. 
Such a miscellaneous class points to the tentative char- 
acter of the classification which the division reflects. A 
violation of the second rule leads to cross-division and 
is the consequence of the employment of more than one 
basis of division. The division of the citizens of a coun- 
try into the rich, the poor, and the educated is an ex- 
ample of cross-division. 

Forms of Division. There are two forms of di- 
vision, dichotomous and classificatory division. These 
are readily distinguishable. In dichotomous, or bifur- 
cate, division the genus is cut into two classes, those 
which possess the character and those which do not. 
The one is a positive group, the other is an indefinite, 
negative group. Together, however, they are exhaus- 
tive of the genus. This process can be further continued 
on either of the two groups. The other form of division, 



CLASSIFICATION AND DIVISION 59 

which I have called ' classificatory,' is the reverse aspect 
of any system of classification. The species into which the 
genus divides are positive and coordinate ; their num- 
ber is determined by the nature of the field. We may 
speak of such division as ' analytic ' and of the corre- 
sponding classification as ' synthetic.' 

Dichotomous Division. While dichotomous divi- 
sion is simple and exhaustive, it easily becomes unwieldy 
when carried far. Moreover, one side is negative and 
indefinite. All that is known about it is that it lacks 
the positive character the other side possesses. Under 
certain circumstances, however, the lack of a quality 
may be as interesting as its possession. Thus the di- 
vision of the population into voters and non-voters, or 
of the working-classes into skilled and unskilled, gives 
us two groups which are really coordinate. Where we 
are interested in some part of the field rather than in 
the whole, tracing by dichotomy may be the easiest 
way. The following example, usually called the ' Tree 
of Porphyry,' makes the method clear : — 

Substance 



Corporeal Incorporeal 



Animate Inanimate 

A 



Sensible Insensible 

/\ k 



Rational Irrational 
/\ 



— v 
Mortal Immortal 



This method of division mav be made instrumental 
to the working-out of a definition of a term. Thus, ac- 
cepting the adequacy of the above tree, we can define 
man as 'a corporeal substance, animate, sensible, ra- 
tional, and mortal.' Another example will serve to 



60 THE ESSENTIALS OF LOGIC 

bring out this use sufficiently. " The term to be defined 
is ' tuber ' ; the genus to which it is to be referred is 
4 stem.' 

Stem 



creeping not creeping 



underground not underground 



much thickened not much thickened 



possessing leaf-buds not possessing leaf-buds 

in the form of ' eyes ' in the form of * eyes ' 

" In this division, we reach, as our definition of a 
tuber, 6 a stem creeping underground, much thickened, 
and possessing leaf-buds in the form of eyes/ " * 

Classificatory Division. This form of division is, 
in its final expression, the same as a system of classifica- 
tion. The species under any genus must be coordinate 
and exhaustive. It should be remembered that the move- 
ment in division is downward from the general to the 
more particular, while in classification it is upward from 
the particulars to the more general. Only one other 
point needs, I think, to be mentioned. The funda- 
mentum divisionis which is selected depends partly 
upon the purpose, partly upon the character of the 
subject-matter. 

Dangers to be guarded against. Imperfect classi- 
fication and division lead to the identification of things 
and ideas which should be discriminated. This is, as we 
have seen, the chief cause of ambiguity. It is, in fact, 
impossible to treat definition and ambiguity apart from 
the consideration of classification and division, for in 
these processes we are studying the methods by which 

1 Joseph, An Introduction to Logic, p. 113. 



CLASSIFICATION AND DIVISION 61 

the mind orders and arranges its material. For the ma- 
jority, an examination of the systems established in the 
various sciences is of less value than the critical analy- 
sis of less formal and better-known subjects. The chief 
danger to be guarded against is the merging together 
of things which should be distinguished. Natural law 
should not be confused with moral law, nor this with 
statute law. Education should not be identified with 
erudition, nor cleverness with talent. 'Democracy' 
should not be used as a blanket-term to cover repre- 
sentative institutions and the absence of caste. The 
proper use of terms is the result of the critical discrimi- 
nation of different meanings, and these meanings them- 
selves rest upon the keen perception and exhaustive 
treatment of likenesses and differences. After classifica- 
tion comes definition which is its fruition. 

REFERENCES 

Creighton, An Introductory Logic, chap. v. 
Hibben, Logic, Deductive and Inductive, chap. VI. 
Jones, Logic, Inductive and Deductive, chap. ill. 
Joseph, An Introduction to Logic, chap. v. 
Minto, Logic, Inductive and Deductive, part II, chap. I. 
Schiller, Formal Logic, chap. vi. 



CHAPTER VI 

PRINCIPLES OF DEFINITION 

Why Definition is Needed. In a former chapter 
we saw why language is a necessary instrument of 
thought and what some of its imperfections are. " The 
logical ideal of the relation between words and thoughts 
is, of course, that every thought should have its own 
name, and every name should have its own meaning." 1 
This ideal is unrealizable because language is always 
changing. New shades of meaning are constantly being 
developed and old distinctions falling into disuse. But 
ignorance and mental indolence are also at work to make 
the use of words unclear. The correct employment of 
words depends upon three things : a large vocabulary, 
a fund of clear meanings, and the proper adjustment 
of the two* Unless these three things are forthcom- 
ing, there will be confusion in the individual's mind 
and misunderstanding when he attempts to communi- 
cate his ideas. Probably John Locke has pointed out 
these dangers, which only definition can correct, as well 
as any one : — 

" For he that shall well consider the errors and ob- 
scurity, the mistakes and confusion, that are spread in 
the world by an ill use of words, will find some reason 
to doubt whether language, as it has been employed, has 
contributed more to the improvement or hindrance of 
knowledge amongst mankind. How many are there, that, 
1 Davidson, The Logic of Definition, p. 2. 



PRINCIPLES OF DEFINITION 63 

when they would think on things, fix their thoughts 
only on words, especially when they would apply their 
minds to moral matters ; and who, then, can wonder if 
the result of such contemplations and reasonings about 
little more than sounds, whilst the ideas they annex to 
them are very confused and very unsteady, or perhaps 
none at all ; who can wonder, I say, that such thoughts 
and reasonings end in nothing but obscurity and mis- 
take, without any clear judgment or knowledge ? " * 

We have said that definition can be of great assist- 
ance in overcoming such confusion and misunderstand- 
ing. But definition is a process which works with words 
and ideas. The individual must be capable of handling 
thousands of concepts and of distinguishing nice shades 
of meaning ; he must also have a fairly large fund of 
knowledge. On the verbal side, he must be able to dis- 
criminate the uses of words. These are really two as- 
pects of the same process, for I very much doubt whether 
the Mrs. Malaprops are much more sensible in their use 
of ideas than in their use of words. No one can make 
nice discriminations between words who cannot do the 
same for ideas. Both acts are achievements which do 
not come without effort and the establishment of good 
mental habits. And it is the belief of the logician that 
the study of logic should assist in the formation of such 
habits. It stresses the need and gives the general rules 
and methods which should be followed. 

The Purpose and Nature of Definition. Defini- 
tion has a double aspect. On the one hand, terms are 
defined in order to test correspondence in the use of 
words. Two disputants wish to discover, for example, 
1 Essay concerning Human Understanding, bk. in, chap. xi. 



64 THE ESSENTIALS OF LOGIC 

whether they have the same understanding for a pivotal 
word. If they do have, they can profitably proceed in 
their discussion ; if they do not have the same idea, they 
must go further back until they find some common 
ground of agreement. On the other hand, definition 
arises as the temporary completion of a field of investi- 
gation. A definition is a summary in which ideas are 
ordered in relation to one another. A definition is a 
product just as the meanings concerned are products. 
Looked at in this genetic way, definitions are seen to 
be tentative. 

There are two aspects to every definition because both 
ideas and words are involved. Ideas must be achieved 
and analyzed, and the meaning obtained must be at- 
tached to a word as its meaning. According to the set- 
ting, either of these aspects may be emphasized more 
than the other. Logic has recognized this possibility in 
the distinction between real and verbal definitions. 
When the purpose is, predominantly, to indicate how 
we intend to use a term, the result is a verbal definition. 
Dictionary definitions are of assistance here because 
they offer the average or common meaning. It must be 
remembered that the peculiar purpose or point of view 
of the individual enters in to qualify the average mean- 
ing, which is in many ways an abstraction. Verbal defi- 
nitions represent past achievements. When, on the other 
hand, we are interested primarily in getting an ade- 
quate idea, we are said to achieve real definitions. We 
try to get behind words to the things and concepts for 
which they stand. 

To define is, then, to indicate the meaning of a word 
by achieving an analyzed concept. Definition is an at- 



PRINCIPLES OF DEFINITION 65 

tempt to attain to a definite meaning. On the mental 
side, it is largely an outgrowth of classification and 
division. 

Logic stresses General Terms. Logic has been so 
impressed by scientific method that it has connected 
definition with classification and division. It is for this 
reason that writers in logic usually define definition as 
the process of determining the connotation of a term. 
It will be remembered that general or class terms have 
two aspects, the things to which they apply and the at- 
tributes which they imply. To define such a term is to 
state the attributes characteristic of the class and, indi- 
rectly, to establish its denotation. 

It is because vague terms become ambiguous that the 
need for definition is felt. We wish to know exactly 
what a term stands for. For example, is a ' communist ' 
the same as a i communard' ? Now, in the case of proper 
names the ambiguity can be overcome by pointing to 
the person meant or by adding descriptive words to 
make the reference definite. Much the same process is 
necessary for abstract terms which are simple. If a man 
asks me what 'redness' means, I can only reply by call- 
ing his attention to some red object and indicating the 
quality. I must assume his ability to abstract the qual- 
ity and make it an object of thought. But the applica- 
tion of class terms cannot be indicated in this simple 
fashion. It is true that I can illustrate the use of such 
a term by an example or specimen. " But any example 
might illustrate a variety of things ; if two persons, each 
of whom was entirely unacquainted with the language 
of the other, should try to communicate by pointing to 
objects to indicate the meaning of the words they were 



66 THE ESSENTIALS OF LOGIC 

using, they would illustrate the uncertainly of this method 
in its extreme form. If one of them should point to a 
horse, he might mean any one of a dozen different 
things : horse, or simply animal, or useful animal, or 
large object, or gray, or beautiful, or dangerous, and so 
on. x 

Definition and Classification. It can readily be 
seen that real definition, or the process of securing 
clearer and more adequate ideas, is bound up with the 
logic of classification. To obtain a clear idea of a class 
we must see it as a part of a system. Thus the defini- 
tion of a triangle, 4 as that section of a cone which is 
formed by a plane passing through the vortex perpen- 
dicularly to the base,' reveals the triangle as related to 
a system of geometrical objects. The more scientific a 
definition, the more it is the reflection of a classified 
field. Definition is possible only when there is organized 
knowledge. In a very true sense, the whole of logic 
concerns itself with the method of obtaining well-defined 
ideas. 

The Verification of Meaning. The verification of 
the meaning of a term is partly a social process, partly 
a process of investigation of the things, actions, or 
events indicated by the term. There is always a rough 
approximation of the meaning with which to begin. 
The problem is to narrow down and define the use. 
Take, for example, such words as ' freedom,' ' liberty,' 
'justice,' and 'equality.' These words are often on 
people's lips, yet they are used vaguely. They refer to 
the same social field, but stress different aspects of that 
field. They are allied while at the same time distinct. 
1 Jones, Logic, Inductive and Deductive, p. 58. 



PRINCIPLES OF DEFINITION 67 

What must be done in order to verify their proper 
meanings ? 

There are two levels in the verification of meaning. 
The first is to determine how the word is actually used ; 
the second is to advance to a scientific concept which 
fits into a thoroughly classified and analyzed depart- 
ment of investigation. The first level gives us a clear 
popular concept ; the second, if successful, gives us a 
scientific concept. It goes without saying, however, that 
the scientific concept is essentially a summary of the 
total field under investigation. It is difficult, if not im- 
possible, to get a clear vision of its contents and impli- 
cations apkrt from an intimate acquaintance with the 
field. Let the reader pick up a book on a subject with 
which he is not familiar and attempt to understand the 
technical terms while neglecting the facts and argument 
with which they are connected, and he will understand 
that the verification of scientific concepts is one with 
scientific investigation itself. 

But logic is also concerned with a more general play 
of the mind which works for clear meanings whether 
at the level of common sense or at that of science. It 
can never be amiss to run over the denotation of a term 
and to discuss with others their understanding of its 
exact shade of meaning. The more complex the field, 
the more valuable is this practice. This method of veri- 
fication goes back to the Greeks, who made much use 
of it when they realized how uncertainly terms are em- 
ployed by the majority of men. Socrates crystallized 
this procedure and it has consequently been called ' So- 
cratic induction ' and c Socratic dialectic ' according as 
stress is laid upon the running over of examples or 



68 THE ESSENTIALS OF LOGIC 

upon the value of free discussion by means of question 
and answer. Every one should read some one at least 
of the earlier Socratic dialogues of Plato in which this 
suggestive method is used as a tool for deepening and 
defining the meanings of common terms. When this 
method is skillfully applied, one can see, as it were, 
meanings grow under one's eyes. Under such condi- 
tions, the definition becomes a living thing into whose 
secrets one is admitted. " The truth is — as most read- 
ers of Plato know, only it is a truth difficult to retain 
and apply — that what we gain by discussing a defini- 
tion is often but slightly represented in the superior 
fitness of the formula that we ultimately adopt ; it con- 
sists chiefly in the greater clearness and fullness in 
which the characteristics of the matter to which the 
formula refers have been brought before the mind in 
the process of seeking for it. . . . In comparing differ- 
ent definitions our aim should be far less to decide 
what we ought to adopt, than to apprehend and duly 
consider the grounds on which each has commended it- 
self to reflective minds. We shall generally find that 
each writer has noted some relation, some resemblance 
or difference, which others have overlooked ; and we 
shall gain in completeness, and often in precision, of 
view by following him in his observations, whether or 
not we follow him in his conclusions." *■ This method is 
especially advisable in the social sciences or in the 
handling of those general topics which arise so fre- 
quently for discussion. How few of us know exactly 
what we mean by such terms as 'nature,' 'justice,' 

1 Sidgwick, Political Economy, pp. 52-53 ; quoted from Minto, Logic, 
Inductive and Deductive, p. 90. 



PRINCIPLES OF DEFINITION 69 

4 law,' ; beauty,' etc. ! Familiarity with the word deceives 
us into the belief that we understand the concept of 
which it is the sign. 

Rules of Definition. The following rules of defini- 
tion should put the student on guard against bad defi- 
nitions and should give him some assistance in his 
attempts to formulate good definitions. All the techni- 
cal terms needed have already been given in the chap- 
ter on " Division and Classification." 

1. A good definition is by proximate genus and 
essential difference. We should try to find a larger 
class with which to connect the thing defined and then 
analyze and state the features of the thing defined 
which distinguish it from the other members of this 
larger class. By relating it to this larger class, we in a 
measure explain it, for we connect it with something 
more familiar. We are then in a position to pass down to 
important differences. This rule of definition brings out 
its intimate connection with classification and division. 

When the difference offered is not essential or is 
vaguely conceived, we have an imperfect definition. Many 
imperfect definitions are suggestive because they reveal 
the fact that the topic concerned has not yet been 
clearly analyzed and classified. 

2. A term shoidd not be defined by means of itself 
or of words which are synonymous with it. We should 
avoid tautology. Dictionaries transgress against this 
obvious rule only too frequently. It is hardly enlight- 
ening to be told that life is a ' vital force,' or that pleas- 
ure is ' agreeable sensation,' or that altruistically is ' in 
an altruistic manner.' 1 More serious cases of defining 

1 For other examples see Davidson, The Logic of Definition, p. 62. 



70 THE ESSENTIALS OF LOGIC 

a thing by itself are the following : ' Life is that which 
distinguishes living from non-living things,' * A cause 
is the invariable and unconditional antecedent of a 
phenomenon.' Relative terms are often defined in terms 
of each other. The consequence is that we go from one 
to the other and then back again and are not greatly 
advanced by the process. 

3. A definition should be neither too broad nor too 
narrow. It should not cover a larger field than usage 
warrants nor a narrower field. Thus, to define a square 
4 as a rectangle,' or a root as i that part of a plant which 
grows underground,' would be cases of overbroad defi- 
nitions ; while to define a dog 4 as a domesticated ani- 
mal used to guard the home ' would obviously be too 
narrow. This rule is really only a development of the 
first rule, for, had the genus and essential difference 
been worked out, the resultant definition would have 
been neither too broad nor too narrow. 

4. A definition should not be expressed in obscure 
or figurative language. The purpose of a definition 
should be kept clearly in mind. Where the field is 
necessarily technical, the use of technical terms is in- 
evitable, and these must not be considered obscure 
however little they are understood by the layman. " The 
scientific definition of life as the dynamic condition of 
an organism would not be that of the plain man. The 
plain man thinks he knows what ivy is, and is not 
much wiser for being told that it is an epiphytic plant 
of the genus hedera. But he, too, may learn something 
from the definition of sickness as Nature's protest 
against the misdirection of her forces, or from St. Aus- 
tin's phrase, ' virtus est ordo amoris ' — the orderly and 



PRINCIPLES OF DEFINITION 71 

progressive unfolding of love." 1 In this connection, Dr. 
Johnson's famous definition of network, as " anything 
reticulated or decussated at equal distances with inter- 
stices between the intersections," is usually given as a 
horrible example of misapplied learning. 

5. A definition should be expressed in positive terms 
whenever possible. A definition should tell what a 
thing is, rather than what it is not. But ultimate con- 
ceptions can often be suggested and indicated by neg- 
ative terms. Thus, a geometer may define a point as 
that which has neither length, breadth, nor thickness. 
We must, however, stress the meaning of a definition 
instead of its form. Where the concept defined is, itself, 
essentially negative, there must be a negative element 
in the definition. ' Liberty is absence of restraint.' 
1 Uncertainty is the want of a fixed mental attitude.' 
4 A bachelor is an unmarried man.' 'Injustice is the 
not keeping of covenant.' These are all negative in 
form, but as positive as their contents permit. 

Other Forms of Definition. We have stressed 
what may be called the ideal form of definition, that 
through genus and differentia. In the Latin terminol- 
ogy of logic it is called definition per proximum genus 
et differentiam vel differentias. It is, as we have con- 
stantly pointed out, the reflection of a system of clas- 
sification. When such a basis cannot be appealed to, 
resort must be had to other methods of making the 
meaning of a term clear. The methods usually adopted 
in such cases are as follows : — 

1. Description. Individual things or events can be 
described in such a way as to make the application of 
1 Macleane, Reason, Thought, and Language, p. 175. 



72 THE ESSENTIALS OF LOGIC 

the term clear. It is possible to select outstanding prop- 
erties or traits which serve to distinguish one thing 
from another. Accurate word-painting is an art which 
can be used to reproduce in the mind of the hearer or 
reader the essential characteristics of the scene or per- 
son described. 

2. Examples. If well-selected examples of the term 
under discussion are given, it is possible to get a pop- 
ular concept, at least, of the term. What does 4 good f 
mean ? How natural it is to run over examples of good 
men ! In doing so, we are trying to pass from the de- 
notation to connotation, a part of the denotation being 
less doubtful than the exact marks which make a man 
good. It depends upon the purpose how far the use of 
example is satisfactory. If this be practical, examples 
may meet the need and thus serve as a sort of defini- 
tion. 

3. Genetic formula. It is frequently important to 
know how a thing is made. Chemical formulae do not 
tell us the essential properties of the thing unless they 
reveal to us a scheme of classification connected with 
such properties. They are, however, of distinct utility. 
Recipes, diagrams, instructions are practical definitions 
of a genetic kind. 

The need lying back of definition is to understand 
the application of a term. Whatever meets this need 
is, in the broadest sense of that term, a definition. 
Hence the logician must not be dogmatic and set up 
only one type of definition. Purpose and setting must 
be taken into account. " In defining we look to what 
appears to be, for our immediate purpose, some striking 
feature. We try to define everything by something 



PRINCIPLES OF DEFINITION 73 

better known. A fox would not be defined in the same 
way by a huntsman and by a naturalist. Death, which 
to the physician is the cessation of all vital functions, 
is to the singer of Hawthornden i the thaw of all those 
vanities which the frost of life holdeth together.' "* 

The Predicables. Logic is a very old science and 
has accumulated traditions and technical names. It is 
hardly justifiable to neglect these inherited distinctions, 
yet they must not be allowed to occupy too much space. 
Typical of this logical tradition are the 6 Five Predi- 
cables.' A predicable is literally that which can be 
predicated. Now, only that which is a general term can 
be predicated of a subject. I can say that this object 
is a cat, but I can't assert of any other object that it 
is this particular object which I have just called a cat. 
In other words, I can't predicate an individual thing of 
another thing. What I can predicate is some attribute 
of the thing. But attributes are of two kinds, defining 
and not-defining. The result is that I discover the fol- 
lowing division of attributes : — 

Attributes 



defining not-defining 

r r 1 1 

generic specific proprium accident 

(differentia) 

These are the Five Heads of Predicables. In relation 
to the subject, the attributes found in the predicate may 
be generic, specific, differential, a constant property, 
and an accident. It is evident that these terms reflect 
classification and division, and this fact brings out once 
1 Macleane, Beason, Thought, and Language, p. 174. 



74 THE ESSENTIALS OF LOGIC 

more the intimate relation between the ideal form of 
definition and these processes. 

The generic attributes give the connotation of the 
genus, while the specific attributes are those which are 
common to the species. It will be remembered that the 
differentia is that attribute, or attributes, which distin- 
guishes one species from its coordinate species. But 
an object may possess, besides, some property not es- 
sential enough to be used as a differentia yet always 
present. When this property is deducible from the de- 
fining attribute it is called a 'proprium.' Attributes 
which sometimes belong to a class of objects and are 
sometimes absent are called 4 accidents.' It is an acci- 
dent that a university is located in one city rather than 
in another; that is, it is no part of the nature of the 
university to have this particular location. It is an ac- 
cident of a thief to be in prison and of a politician to 
be honest. It should be borne in mind, however, that 
the term is here used in connection with classification 
and division. In another sense of the word 6 accident,' 
it may well be that nothing is an accident ; this means 
that every feature of an individual thing has a cause. 

The Importance of Definition. From its very be- 
ginning, logic has stressed the importance of definition. 
It is impossible to think clearly and to avoid ambigui- 
ties without definite ideas and properly applied words. 
The very familiarity of words may lead us to suppose 
that we understand their use, and encourage us in the 
mere manipulation of verbal counters to the neglect of 
concepts. Verbal definition is important, but we must 
never forget that it rests upon ordered knowledge. Or- 
dered knowledge is, however, only another name for 



PRINCIPLES OF DEFINITION 75 

real definition. When we once realize this fact, we im- 
mediately become aware of the importance of definition, 
both as a process and as a result, and of the value to 
the individual of those mental habits of analyzing and 
distinguishing which give structure and clearness of 
outline to his accumulated knowledge. Definition is to 
the mind what discipline is to an army. Without dis- 
cipline, an army is like a mob ; it lacks both unity and 
the means which make unity effective. Without defini- 
tion, the mind lacks differentiation and distinctness in 
its contents. 

EEFERENCES 

Creighton, An Introductory Logic, chap. V. 
Davidson, The Logic of Definition, chap. in. 
Hibben, Logic, Deductive and Inductive, chap. v. 
Jones, Logic, Inductive and Deductive, chap. iv. 
Macleane, Reason, Thought, and Language, chap. xi. 
Schiller, Formal Logic, chap. vi. 



CHAPTER VII 

ASSERTIONS AND PROPOSITIONS 

An Important Distinction. As logic has grown 
less formal and has been more influenced by psychology, 
it has more and more recognized the necessity of draw- 
ing a distinction between assertions and propositions. 
An assertion is a living judgment which expresses the 
conclusion reached by an individual as a result of his 
thinking. ' True patriotism stands for ideals,' and, 6 1 
must take more exercise,' are for me genuine assertions 
which I understand. But when I glance at a list of ex- 
ercises in a logic-text and come across the sentence, ' It 
is hot,' I am not absolutely certain what ' it ' refers to. 
I tend to assume that the weather is referred to, but 
the writer may possibly have had a stove or a cup of 
tea in mind. Such isolated sentences need interpreta- 
tion. The reader must make a judgment out of them 
by his own mental activity. And, as we all know, we 
are sometimes mistaken even when the context is quite 
complete. In contrast to personal, living assertions, 
then, propositions are sentences, or verbal complexes, 
which are supposed to symbolize such assertions ; they 
are bodies into which some mind must breathe the 
breath of life. Propositions can exist on paper, while 
assertions can live only in the mind. 

Under ideal conditions, the propositions put forward 
in actual cases of argumentation may be correct substi- 
tutes for assertions quite capable of conveying to other 



ASSERTIONS AND PROPOSITIONS 77 

minds the exact shade of meaning intended, but such 
is not always the case. Before this transference of 
meaning from one mind to another is possible, there 
must be painstaking effort on the part of the listeners 
to comprehend those who are speaking. How often a 
statement is misunderstood, or, as we are apt to say, 
twisted and distorted ! The whole context, or universe 
of discourse, must be appreciated before a statement is 
given its correct setting. Such a context is present in 
any actual judgment, but it cannot be attached directly 
to the proposition. A sentence, spoken or written, can- 
not contain very much. Take the famous line in Shake- 
speare's Henry VI: " The Duke yet lives that Henry 
shall depose" ; it is obvious that the ambiguity rests in 
our inability to get to the real assertion, assuming that 
there was one. 

When conditions are very favorable, the distinction 
between assertions and propositions can be allowed to 
drop into the background. We suppose that we can 
pass from one to the other with ease. But when propo- 
sitions are given piecemeal and apart from their con- 
text, it is often impossible to interpret them in any 
final sense. Under such conditions we are forced to pay 
attention to certain general aspects which should be 
clear. We change propositions into assertions as com- 
pletely as possible, and then proceed to analyze them. 
But it is always well to bear in mind this important 
distinction. 

Critical vs. Uncritical Assertion. Some mental 
processes are relatively unconscious, while others de- 
mand attention for their very being. We often act and 
speak habitually and imitatively. We do what we have 



78 THE ESSENTIALS OF LOGIC 

been accustomed to do and to see others do, and we say- 
things which come into our heads or which we have 
heard other people say. The ideal of logic is to make 
individuals critical, and this aim is furthered by the 
knowledge it gains of mental processes and of scientific 
methods. But when logic became very formal and gave 
almost its entire attention to propositions taken sepa- 
rately, it became too mechanical to help the individual 
in his concrete thinking. What we shall try to do, then, 
is to explain these older analyses of propositions and 
give them a more vital setting. 

Critical thinking seeks to determine the facts and 
principles of the case, to test both, and then to see 
whether the conclusion drawn is justified. It takes as 
little for granted as possible. It brings all the facts 
and principles into the open. This mental effort criti- 
cally to interpret a case of reasoning which appears 
doubtful, leads to the marshaling of all our resources, 
to the bringing-out of all the facts and rules which 
bear upon the problem, to the analysis of likenesses and 
differences with other cases, to the more patient wait- 
ing for suggestive ideas. The result is usually a more 
adequate solution of the problem with a broader under- 
standing of its meaning. Let me give an instance of 
critical versus uncritical thinking. A student comes to 
me and asks whether logic is a practical subject. I 
know pretty well by past experience what he means by 
the term ' practical.' But I ask him and he replies, ' Is 
it of use in everyday life ? ' Obviously, by everyday 
life he means business life. Will logic help him to suc- 
ceed in his profession? It thus becomes a question of 
the qualifications of a successful business man. I may 



ASSERTIONS AND PROPOSITIONS 79 

deny that his ideal of. success is a wise and adequate 
one, or I may try to show him that whatever makes 
his thinking more accurate and critical has a tendency 
to make him better qualified for business. The student 
has made certain assumptions as shown by the very 
words that he uses ; in fact, he has revealed an outlook 
upon life. 

What is an Assertion ? We may define an asser- 
tion as a mental act and content arising out of and 
concluding a process of interpretation. Such an asser- 
tion is a judgment, a conclusion, a decision. Interpre- 
tations, generalizations, theories, inferences, beliefs, 
views, decisions are present from the early days of a 
child's life, and represent the growing, synthetic side 
of its mind. The growth of the mind, this putting two 
and two together, this recognizing and analyzing and 
comparing, is not a mechanical process. It is remark- 
able how soon the child notices things and seeks to in- 
terpret them. A little girl somewhat less than three 
years old was looking at her teddy-bear and noted for 
the first time the brown, hairless soles of its feet. The 
color struck her attention and she said, " That 's blood." 
Her brother, aged four, gave his judgment. " No, baby, 
that's where the whiskers have come off." Baby re- 
plied, " We must buy some at the store and put them 
back on." 

Of much of this continuous interpretation we are 
not reflectively aware. It does not stand out so clearly 
in consciousness that we remember it and can recall 
the various steps. The individual's field of experience 
seems to him always to have been much the same as it is 
now. Out there is the realm of physical things open to 



80 THE ESSENTIALS OF LOGIC 

inspection ; and these things fall into kinds which are 
usually easily recognizable. In contrast to this common 
world of physical things is the more personal domain 
of the self with its feelings, valuations, and purposes ; 
and there is, finally, the social realm of other minds. 
In other words, the mind of each individual is full of 
implicit assertions which cannot be accounted for apart 
from pretty constant mental activity. Interpretation is 
going on all the time and finds expression in judg- 
ments. These judgments are assertions which deal with 
these recognized realms. When I say, 4 That 's Smith,' 
I mean that the person I see at a certain distance from 
me goes by the name of Smith. When I say, ' Nitrates 
are necessary for the soil in agriculture,' I take the 
physical world for granted and make an assertion about 
certain relations between it and plants. Thus we are 
interested in, and pass judgments about, the world in 
which we live. 

Levels of Judgment. We have taken the term 
« Judgment ' in a broad sense as standing for both the 
process and the act of interpretation. Very often, the 
mental steps just previous to the assertion do not rise 
to the surface of consciousness, We feel certain that 
the person over yonder is Jones, but we don't just know 
why. He gives us the general impression of Jones. 
Only when doubt is cast upon our interpretation of 
our perception do we look more closely and analyze 
this feature and that which are connected in our mind 
with Jones. Perceptual judgments, or judgments bound 
up very closely with what we are perceiving, are of this 
almost intuitive character. 

The more of a problem there is, the more reflective 



ASSERTIONS AND PROPOSITIONS 81 

is judgment. The process of reaching a conclusion now 
takes time, and we are aware of various suggestions and 
steps. We try to find exactly what is given and where 
the difficulty lies, and then ransack our experience to 
find a satisfactory solution. Such a mental process is 
called ' reasoning ' and may take a long time ; but when 
a solution is found, it appears as a judgment. 

It is customary for logicians to classify judgments 
as 'dominantly perceptual' or as 4 dominantly con- 
ceptual.' All judgments involve concepts, however, and 
there is no sharp break between the judgments of per- 
ception and the abstract judgments of history and of 
science. A huge body of facts must be collected, an- 
alyzed, compared, and organized before such abstract 
judgments are possible. In the latter half of the book 
we shall have much to say of these progressive steps 
which raise us to such abstract judgments as ' The plan- 
ets travel in elliptical paths, 5 and 4 Democracy is still in 
process of development.' 

Concepts and Judgment- Judgments always con- 
tain concepts, or meanings. It was this fact that led 
many of the older logicians to think of judgments as 
formed from the union of two concepts. That is now 
seen to be too mechanical an idea. The content of a 
judgment is complex, but it is also unitary; it makes 
up one assertion. 

The relation between concepts and judgment is a 
vital one and can be understood only when approached 
in a genetic way. Concepts are the material of judg- 
ment and are at the same time products of judgment. 
To ask which is prior in any absolute way is like ask- 
ing the old puzzle, Which came first, the hen or the 



82 THE ESSENTIALS OF LOGIC 

egg ? Judgments grow out of conceptual material, but 
this conceptual material is itself the deposit of other 
judgments. Again, this conceptual material is modi- 
fied by judging as a process and exists in an unique way 
in any really new judgment. An example may make 
this clearer. 

Take a person who is visiting an aquarium for the 
first time. Undoubtedly, he has some idea of many of 
the kinds of fish which are on exhibit, but his ideas are 
usually somewhat vague and unsettled. When he comes 
before the tank in which is, for instance, the devil-fish 
or ray, he makes the identification, and, in so doing, 
modifies his concept. It is no longer the hazy concept 
it once was. Again, take the student who comes to col- 
lege. He has a general idea of what a college is for. 
But, as he progresses from the freshman to the senior 
year, he is compelled, by the very pressure of his com- 
plex experience, to pass judgments in which this gen- 
eral ideal is modified, deepened, and enlarged. Judg- 
ment is, in fact, the individual's system of concepts in 
process of adjustment and enlargement. Concepts drop 
into the background so far as consciousness is con- 
cerned and become potential or implicit when they are 
not the living parts of a judgment. 

Judgment defined. There are many definitions of 
judgment, varying slightly in their form or their em- 
phases from one another. Two aspects of every judg- 
ment stand out clearly. There is, first, the complex 
content which is held before the mind, and, second, the 
attitude of belief or acceptance taken toward it. Let 
us look a little more closely at these two aspects. 

Every judgment involves a complex content. What 



ASSERTIONS AND PROPOSITIONS 83 

the content is depends upon the location of the problem 
which gives rise to it. It may be dominantly perceptual 
with just a touch of conception at the point which 
needed interpretation, as when I step outdoors of a 
morning and exclaim, ' It 's a fine day after all ' ; or it 
may be almost equally perceptual and conceptual, as 
when I classify a plant which I run across in my stroll 
through the woods ; or it may be entirely conceptual, as 
in the statement of some law of nature. In every case, 
however, the total content which I hold before my 
mind is complex, the nature of the complexity varying 
with the field involved and the nature of the problem 
to which the judgment is an answer. Sometimes we 
are interested in the qualities of things, sometimes in 
classes and their relations to one another, sometimes in 
comparisons, sometimes in personages and events. The 
character of the content determines the type of judg- 
ment with which we have to deal. 

Again, every judgment involves a mental attitude 
which is that of belief or assertion. As a rule, the 
psychologist prefers the term ' belief,' while the logician 
speaks of 4 assertion.' The content is believed or asserted 
to hold of the realm which is under discussion. When 
we use the term • belief,' we keep a more personal 
reference. ' It is my belief, or my judgment, that Napo- 
leon was a worn-out man by the time of the Russian 
campaign.' Here a complex idea concerning itself with 
European history of somewhat over a century ago is 
accepted as true. I feel constrained by the pressure of 
the facts to think of Napoleon in this way. This mental 
constraint which arises out of the facts, says the logi- 
cian, leads me to make the assertion, 'Napoleon was a 



84 THE ESSENTIALS OF LOGIC 

worn-out man,' etc. Napoleon and the Europe of his 
day are objects before my mind's eye, and I determine 
to think of one feature, which has been open to ques- 
tion, in this way rather than in that. The rest of my 
knowledge furnishes the setting for this once moot 
point which I now take to be settled. 

A judgment is, then, a complex mental content which 
is asserted or toward which we take the attitude of 
belief. Such an assertion must be either true or false. 
It is this concern with truth or falsity which is distinc- 
tive of a judgment. In language, this characteristic 
finds expression in the indicative mood in contrast to 
commands, wishes, and questions. The reason for this 
difference rests ultimately in the fact that knowledge 
is claimed or assumed in the one form, while not in 
the others. When I ask a question, I request some one 
else to make an assertion, but do not myself make one. 
When I issue a command, I am concerned with an 
action which I am trying to bring about. In neither 
case am I expressing a belief. 

All Knowledge Judgmental. We have stressed 
the fact that live judgments spring from problems. But 
such problems must always be local or concern points of 
doubt within a larger field about which there is, for the 
time being, no question. This larger field which fur- 
nishes the setting of the new judgment is itself, how- 
ever, the product of the continuously accumulating 
judgments of the mind and the content of the new 
judgment is knit to it like new cells in a growing or- 
ganism to the old. It is strictly true to say that all our 
knowledge has been, at one time or other, a part of the 
content of a judgment and that it is more or less im- 



ASSERTIONS AND PROPOSITIONS 85 

plied as a foundation for the new judgment. For this 
reason it must be ready to defend itself and to pass 
from a potential, or passive condition, to the center of 
the mental stage. Each of us possesses a system of con- 
cepts which has been the growth of years of guided 
and unguided mental effort. This system controls our 
thinking and is in turn controlled by it. Only a small 
part of it can appear overtly in the field of attention at 
any one time, but we have good reason to believe that 
all of it is there in a more or less effective way. 

It is this implication of a larger setting for any new 
judgment, a setting which is usually more implicit than 
explicit, that the philosophical logician always stresses. 
And it is well to remember that logic is, after all, a 
philosophical discipline. I make no apology, therefore, 
for the introduction of the following quotation from 
Bosanquet : " We may then sum up so far : our knowl- 
edge, or our world in knowledge, exists for us as a 
judgment, that is, as an affirmation in which our present 
perception is amplified by an ideal interpretation which 
is identified with it. This interpretation or enlargement 
claims necessity or universality, and is therefore objec- 
tive as our world, i.e., is what we are obliged to think, 
and what we are all obliged to think. The whole system 
in process of construction, viz., our present perception 
as extended by interpretation, is what we mean by 
reality, only with a reservation in favour of forms of 
experience which are not intellectual at all. Every judg- 
ment then affirms something to be real, and therefore 
affirms reality to be defined, in part, by that something. 
Knowledge exists in the form of affirmations about 
reality. And our world as existing for us in the medium 



86 THE ESSENTIALS OF LOGIC 

of knowledge consists, for us, of a standing affirmation 
about reality," l 

It is for theory of knowledge to decide tlie character 
of knowledge and its relation to reality, while it is the 
function of metaphysics to determine the nature of 
reality. Logic takes both knowledge and reality for 
granted, and investigates the empirical question of how 
knowledge is actually built up and sustained by human 
minds. The conclusion which is forced upon us is that 
all knowledge is judgmental and is that which we are 
constrained to think by the pressure of our experience. 

The Part played by Language. The actual oper- 
ation of judging is often hard to recover. The modern 
logician, working hand in hand with the psychologist, 
is more and more convinced that this operation is not 
truly reflected in the verbal form which is called the 
proposition. So far as consciousness goes, the mental 
operation is usually simpler than the verbal form. 
Language is more analytic and detailed than the think- 
ing of any one moment. There are two reasons for 
this. Language is used for communication and re- 
flects all the distinctions painstakingly made in the 
past. The other reason lies deeper, language is a 
mechanism and, while instrumental to thought, is not 
identical with it. This disunion came out clearly in 
several of the preceding chapters, especially in the 
chapters entitled " Ambiguity and Language " and 
"Principles of Definition." It would be impossible 
for any mechanism to equal the fluidity and organic 
unity of thought. We must not take the skeleton for 
the living animal. Consciousness is a qualitative com- 
1 The Essentials of Logic, p. 32. 



ASSERTIONS AND PROPOSITIONS 87 

plex in which purpose, context, perception, and the 
whole apperceptive background of accumulated ex- 
perience somehow coexist in a forward movement of 
interpretation. Language, on the other hand, is spread 
out in space and time, and necessarily adapts itself to 
this process of extension. The purpose of language is 
not to reflect the actual genesis of a thought, but to 
express the result in a comprehensible way. An argu- 
ment should be capable of explicit formulation in such 
a way as to give the conclusion in relation to its 
grounds. So far as logic is a science of proof, it deals 
with the overt and not with the hidden ; and the overt 
must find expression in language. 

The Logical Treatment of Propositions. Mod- 
ern logic tries to be as concrete and flexible as possible. 
It insists upon a study of the context to determine the 
point of view of the person who enunciated a given 
proposition. But within such a setting, or, as it is 
called, universe of discourse, a proposition or group of 
propositions is a bit of supposed knowledge which has 
to stand by itself as does a work of art which has once 
left the atelier of the master for the gallery. The 
proposition, as treated by the logician, is an instrument 
of analysis much as a sensation is for the modern psy- 
chologist. The student must be warned that the tradi- 
tional analysis of the proposition to which we now pass 
is dominated by the mechanism of the syllogism and 
the idea of class relations which finds expression therein. 
For this reason, the ' logical form ' of propositions is 
often a procrustean bed for propositions which do not 
naturally express class relations. The art side of logic 
will come to the fore in the next few chapters. 



88 THE ESSENTIALS OF LOGIC 

REFERENCES 

Bosanquet, The Essentials of Logic, Lecture rv. 
Dewey, How We Think, part n, chap. Vin. 
James, Principles of Psychology, vol. n, chap. xxi. 
Minto, Logic, Inductive and Deductive, part I, chap. II. 
Schiller, Formal Logic, chap. Vin. 



CHAPTER VIII 

THE LOGIC OF PROPOSITIONS 

A General Division of Propositions. Proposi- 
tions are divided into ' categorical,' 4 hypothetical,' and 
4 disjunctive.' A proposition is said to be categori- 
cal when it makes a direct assertion. In it a predicate 
is denied or affirmed of a subject. 6 The Romans were 
a strong race,' and ' Dead men don't bite,' are examples. 
A hypothetical proposition combines a condition with 
a consequent. If the condition is fulfilled, the conse- 
quent is held to be true. ' If the great war continues, 
the nations will be near bankruptcy,' and ' If there is 
an early frost, the peach crop will be spoiled,' are cases 
in point. A disjunctive proposition asserts that one of 
two or more alternatives is true. ' Man is either mortal 
or immortal,' and ; This rock is either marble or 
quartz,' are disjunctive in character. 

The categorical type of proposition with its direct 
assertion is the simplest of the three forms and is 
always examined in logic before the others. It is the 
basis of the categorical syllogism. We shall take up 
the other types for discussion afterwards. 

The Quality and Quantity of Propositions. Cate- 
gorical propositions are classified according to quantity 
and quality. As regards quantity, they are either sin- 
gular, or particular, or universal. The quantity of a 
proposition is an aspect of the subject term. If the 
subject denotes only one individual, the proposition is 



90 THE ESSENTIALS OF LOGIC 

said to be singular] if it denotes all the members of a 
class, universal ; if only some members of the class are 
denoted, particular. ' Abraham Lincoln was a sagacious 
statesman ' is a singular proposition because the subject 
term denotes only one individual. ' Some vines bear 
edible fruit ' is a particular proposition because the 
subject term covers only a part of the class. The word 
'some,' or an equivalent, is the sign of a particular 
proposition. 'All citizens are entitled to a vote' is a 
universal proposition. Its sign is 6 all ' or « no ' Q none '), 
or an equivalent. 

The quantity of a proposition is not always definitely 
indicated by the appropriate logical sign. When this 
is the case, the proposition is called 4 indefinite ' or 
4 preindesignate.' The first task of the logician is to 
determine the quantity of such an assertion, for a 
really indefinite proposition is ambiguous and can have 
no place in an argument until its ambiguity is removed. 
Since the mechanism of the syllogism stresses quantity, 
it is absolutely necessary to classify an assertion before 
it can be used as a premise. The following examples 
will show how frequently propositions are left with 
their quantity implicit and even uncertain : — 

* Uneasy lies the head that wears a crown/ 
' Every single day has its blessing.' 

* All flesh is not the same flesh.' 

' The race is not always to the swift.' 
'Haste makes waste.' 

* A man 'c a man for all that.' 

It is necessary to penetrate beneath the verbal form 
to the meaning and decide the denotation of the sub- 
ject term. 



THE LOGIC OF PROPOSITIONS 91 

Quality, when applied to propositions, is a term 
which refers to their character as affirmative or 
negative. An affirmative proposition asserts a predi- 
cate of a subject, while a negative denies it. The 
distinction is too familiar and ultimate to require elu- 
cidation. There are, however, certain dangers in inter- 
pretation which must be guarded against. The mere 
presence of a negative word in a proposition does not 
necessarily make it negative in quality. Such a word 
may be a part of either the subject or the predicate 
term. Only when the negative element involves the 
assertion of a relation of exclusion between the com- 
ponent terms is the quality negative. Take the prop- 
osition, 6 Those who do not use their opportunities are 
unwise.' This is affirmative in quality because a posi- 
tive relation between the two terms is asserted. Whether 
the subject or the predicate is positive or negative does 
not affect the quality of the proposition. 

Symbolic Classification of Propositions. For 
the sake of easy handling, logic has classified all cate- 
gorical propositions into four kinds according to their 
quantity and quality. This treatment has the syllogism 
for its end in view. While it is artificial and one-sided, 
it is convenient and often leads to a better understand- 
ing of the import of the propositions. These four kinds 
are, ' universal affirmative,' ' universal negative,' ' par- 
ticular affirmative,' and ' particular negative.' To sym- 
bolize these the vowels A, E, I, and O are used. A 
and /stand for the universal and particular affirma- 
tive respectively, and are taken from the Latin affirmo ; 
E and O stand for the universal and particular nega- 
tive, and are taken from nego. It should be noted 



92 THE ESSENTIALS OF LOGIC 

that the singular proposition is considered a universal. 
It can be treated as such in the syllogism. Taking S 
and P for the subject term and predicate term re- 
spectively, we have the following classification : — 

< Affirmative : All S is P. A 

Universal < XT , . XT . n ™ 

( Negative : is o S is P. E 

. r Affirmative : Some Sis P. I 

\ Negative : Some S is not P. 

Reduction of Propositions to Logical Form. 

The reduction of the varied statements of ordinary life 
to a form corresponding to this symbolism is a practi- 
cal exercise which has some value. How much it is 
very hard to tell. " The indirect use is to familiarize us 
with what the forms of common speech imply, and thus 
strengthen the intellect for interpreting the condensed 
and elliptical expression in which common speech 
abounds." 2 Such an interpretation is often difficult. 
For instance, it is not always easy to decide whether a 
sentence is particular or universal, affirmative or nega- 
tive. Take such sentences as the following and decide 
into which of the four kinds they fall : — 

' A flower is a beautiful object.' 

* Few were saved.' 

* Women are jealous.' 

' Only ignorant persons bold sucb opinions.' 

The reduction of statements to logical form meets 
with three classes of difficulties. The statement may be 
ambiguous because of the grammatical order of its parts 
or because of the character of certain of its terms ; or 
it may contain a reference to time. Let us look at these 
three classes in some detail. 

1 Minto, Logic, Inductive and Deductive, p. 69. 



THE LOGIC OF PROPOSITIONS 93 

The order of subject and predicate may be inverted. 
* Wide is man's mind ' is an example of such inversion. 
The problem is so simple that there is no need to dwell 
on it. Again, a clause may be separated from the word 
it modifies ; for example, 6 He jests at scars who never 
felt a wound.' In such cases the only rule is to pene- 
trate to the exact meaning. Lastly, some compound 
sentences really contain more than one proposition. 

In the second class come partitive, exclusive, and 
exceptive propositions. A partitive proposition is one 
which makes a statement about one part of a class and 
implies another statement about the rest. There is, then, 
a sort of double meaning. Such words as ' all . . . not,' 
4 some,' * a few,' etc., involve this ambiguity and double 
significance. ' All these children are not of school age ' 
means that some are not, and, probably, that some are. 
Accent plays some part here. l Few are chosen ' means 
that most are not chosen. 

An exclusive proposition is one which is introduced 
by such words as 4 only,' ' none but,' c alone,' and the 
like. 'None but ticket-holders are admitted' is a typi- 
cal exclusive proposition. This means that all those who 
are not ticket-holders are not admitted. Thus the ref- 
erence is to those who do not belong to the privileged 
class. As so interpreted, it is an E proposition. But it 
may also be treated as an A proposition by interchanging 
subject and predicate : 4 All who are admitted are ticket- 
holders.' The old predicate lies within the subject-class. 
An exceptive proposition is one which makes a state- 
ment of all the members except certain designated ones. 
Such sentences are introduced by such expressions as 
* all but,' ; all except,' etc. ' All but the very poor enjoy 



94 THE ESSENTIALS OF LOGIC 

liberty ' is an example. Two statements are usually in- 
volved : ' All who are not very poor enjoy liberty,' and 
4 All who are very poor do not enjoy liberty.' The first 
of these is more certainly implied than the second. It 
is therefore best to restate the proposition dropping out 
the exceptive particle. 

The third class of difficulties is technical in character. 
The logical form, * 8 is i 3 ,' is the statement of a rela- 
tion between classes and does not express either time or 
modality. The customary way is to throw this verbal 
element into the predicate. Thus, 4 The soldiers had 
retreated ' becomes ' The soldiers are in the class of 
those who had retreated,' and 4 It may rain ' becomes 
i Earning is an event which may occur.' When we are 
trying to bring out class relationships, we must not be 
affrighted by the clumsiness of the result. 

The Distribution of Terms. The logical form 
stresses the denotation of the subject and predicate 
terms. If, in a proposition, an assertion is made about 
the entire denotation of a class, the term indicating that 
class is said to be ' distributed ' ; if it is made of only a 
part of the class, the term is ' undistributed. 9 The dis- 
tribution of the terms in the four kinds of categorical 
propositions has been worked out and is, besides, pretty 
obvious. The universal affirmative distributes only the 
subject term. Thus in the sentence, 4 All mammals are 
vertebrates,' the assertion is made of every mammal, 
but there is no corresponding reference to the whole 
class of vertebrates. We have the right to say only that 
some vertebrates are mammals. The particular affirm- 
ative distributes neither the subject nor the predicate 
term. i Some men are loyal' is an /proposition, and 



THE LOGIC OF PROPOSITIONS 95 

there is in this no reference to the entire denotation of 
either class. Turning to negative propositions, we find 
that an E 'proposition distributes both terms. Both 
terms are entirely excluded from one another, and this 
means that there is some knowledge about all the mem- 
bers of both classes, just enough to validate this exclu- 
sion. ' No man is perfect ' informs us that not a single 
man is perfect, and that not a single perfect being is a 
man. Lastly, an O proposition distributes the predi- 
cate and does not distribute the subject. i Some men 
are not honest ' tells us something only about some men, 
but we must know something about all individuals who 
are honest in order to know that some men are totally 
excluded. Examining the distribution of the terms in 
the four kinds of propositions, we find the following 
rule : negative propositions distribute their predicates, 
while affirmative propositions distribute only the sub- 
ject and this only when the proposition is universal. 

The Graphical Method. The relation between the 
subject and the predicate, as regards their denotation 
and the distribution of each term, can be graphically 
represented for the four kinds of propositions by Euler's 
method. If each term be represented by a circle, the 
result is as follows : For A, — 
#, the subject class, is seen to fall en- 
tirely within P, the pred- 
icate class, for the vast 
majority of cases. (Fig. 
1.) Only in the case of 
definitions, in which the two classes co- 
Flg ' 2, incide, do we find the relation that of 

Fig. 2. The shading shows the distribution. 





96 



THE ESSENTIALS OF LOGIC 



For^, 





Fig. 3. 



S falls entirely outside P. Both terms are distributed, 
For L — 




Fig. 4. 



S and P overlap. Neither term is distributed. 
For O,— 




■vFig.5. 

some S is known to be excluded by P. The predicate 
term is distributed. 

Euler's method is applicable to the syllogism also. 
Hence it is well to become familiar with this graphical 
treatment of the denotative aspect of propositions. 

The Purpose of Logical Analysis. This manipu- 
lation of sentences will undoubtedly strike the reader 
as artificial. When we say, 6 All men are mortal,' we 



THE LOGIC OF PROPOSITIONS 97 

do not mean that men are in the class of mortal beings. 
We think of the predicate in its connotation rather than 
in its denotation. But there is a purpose back of this 
stress upon denotation and class relationships, that of 
syllogistic analysis and testing. The ; logical form ' is the 
syllogistic form. When the modern logician is not in- 
tent upon proof, he tries to understand the exact shade 
of meaning and the exact character of the relation pres- 
ent in a proposition. He seeks to classify propositions 
into natural types corresponding to levels of knowledge 
and reflection. But as a syllogizer, he is a specialist in- 
tent upon his method and bending everything to it. He 
then selects one aspect of propositions and moulds them 
in such a way as to bring out this aspect most clearly. 
4 All S is JP' means that 'All S is contained in JFV 
It is the denotation of related classes that he has in 
mind. For a few chapters we shall be dominated by this 
purpose, and the student should bear this fact in mind 
if he cannot always see the importance of certain rather 
formal processes. The means secure their value from the 
end and are as valuable as the end. But it can further 
be said that the thorough study of the denotative aspect 
of categorical propositions cannot help but increase our 
understanding of their reach and meaning. 

REFERENCES 

Creighton, An Introductory Logic, chap. VI. 

Jones, Logic, Inductive and Deductive, chap. V. 

Keynes, Formal Logic, part n, chap. i. 

Minto, Logic, Inductive and Deductive, part I, chap. II. 

Taylor, Elementary Logic, chap. vn. 



CHAPTEK IX 

THE IMPLICATIONS OF PROPOSITIONS 

Immediate Inference. Since the proposition is for 
the logician the unit of knowledge, he wishes to ex- 
haust its meaning. He studies a proposition with the 
express purpose of finding out all that it implies. Now, 
it has been found that we can pass from one proposi- 
tion to others containing the same two terms or their 
contradictories. Thus, ' All men are rational ' enables 
us to say also that c No men are irrational ' and ' No 
irrational beings are men.' Such a passage from one 
proposition to others is called 'immediate inference.' 
The logician has usually been less concerned with the 
mental processes involved than with the validity and 
formal mechanism of the step. 

Let us recall the distinction between a judgment and 
a proposition. A proposition is the verbal expression 
of a judgment. It is usually more stereotyped than the 
living judgment and practically always stresses some 
one aspect of the situation to the exclusion of others. 
Once a proposition is formulated, however, we can go 
back over it and analyze it, turn it about and see it 
from different angles. Thus, when I make the asser- 
tion, ' This book is on the desk,' I can afterwards note 
that ' The desk must be under the book.' Such a 
spatial relation has a double direction. Only one di- 
rection is brought out in the original proposition, but 
I realize that the other, also, exists. In like manner, as 



THE IMPLICATIONS OF PROPOSITIONS 99 

we shall see, the logical form to which the logician re- 
duces categorical propositions stresses a relation be- 
tween terms and the denotation of these terms. The 
consequence is that other propositions can be seen to 
follow from any one formulation. 

But because other propositions can be asserted on 
the basis of a given proposition, it does not follow that 
these other propositions present themselves without any 
mental effort on the part of the thinker. Immediate 
inference is not immediate in the sense that it is intui- 
tive. The nature of the relations must be clearly grasped 
before such implications can be quickly drawn. It is 
for this reason that logical analysis is of value. Only 
one who has mastered this analysis can answer such 
questions as those given at the end of the chapter. 
Why, then, does the logician speak of the development 
of the implications of propositions as ' immediate infer- 
ence ' ? Because he has in mind, as a contrast, the draw- 
ing of a conclusion from the putting together of two 
other propositions called ' premises.' In other words, 
the historical contrast is with the syllogism and its dif- 
ferent mechanism. 

There axe/our headings under which different kinds 
of immediate inference are brought: 'Opposition/ 
* Conversion,' ' Ob version,' and 'Contraposition.' We 
shall now examine these in order and as briefly as is 
consonant with completeness and clearness. 

The Oppositions of the Four Kinds of Propo- 
sitions. Propositions are said to be opposed when they 
have the same terms as subject and predicate, but dif- 
fer in quantity, or in quality, or in both. Within the 
setting given by the logic of propositions, we are able 



100 



THE ESSENTIALS OF LOGIC 



to note certain relations of inclusion and exclusion 
which such statements bear to one another. The study 
of these relations will give us a better idea of the reach 
of each kind of proposition. It will likewise teach us 
how to establish each kind and what its denial implies. 
If the symbols of the four kinds of propositions be 
placed at the four corners of a square with the uni- 
versal at the top and the corresponding particulars at 
the bottom, we shall obtain the so-called ' Square of 

Opposition.' The 

Contraries .El sides and diago- 

nals of this square 
represent relations 
between A, E, I, 
and O. Close in- 
spection has re- 
vealed four kinds 
of relation among 
them : — 

A and E are 
called 'contraries/ 
They differ in qual- 
ity while the same 
If we examine them 
that both may be 




Fig. 6. 



in quantity, both being universal. 

in relation to each other, we find 

false while only one can be true. Thus, 'All swans 

are white' and 'No swans are white' are contraries. 

They cannot both be true, yet they may both be false. 

As a matter of fact, we know that some swans are 

white while others are black. 

A and 0, E and /, are called ' contradictories.' They 
differ in both quantity and quality. Thus the members 



THE IMPLICATIONS OF PROPOSITIONS 101 

of these couples are exact opposites. One must be true 
and the other false. 4 All politicians are honest ' and 
4 Some politicians are not honest ' are contradictories. 
They cannot both be true nor both false. It follows 
that the assertion of I involves the denial of E, and 
the denial of A the assertion of 0. 

I and O are called ' subcontraries.' They agree in 
quantity and differ in quality. Both may be true, but 
both cannot be false. ' Some men are brave ' and 4 Some 
men are not brave ' are subcontraries. Our experience 
tells us that both these propositions are true. When, 
however, we are able to state a universal, the one sub- 
contrary is true, while the other, which is the contra- 
dictory of the universal, is false. 

A and i", E and 0, are called 6 subalterns.' They 
agree in quality, but differ in quantity. Subalterns are 
both true when the universal is true. When the con- 
trary universal is true, both subalterns are false. 6 All 
men are rational' and 'Some men are rational' are 
subalterns. 

It is a good exercise, to test the recognition of these 
interrelations, to start with the truth of any one kind 
of proposition and determine what follows for the other 
three. Granted E, I must be false as its contradictory, 
O must be true as its subaltern, and A must be false 
as its contrary. If we deny E, we automatically affirm 
I. It should be noted that common speech talks of 
contradiction whether we affirm the contrary or the 
contradictory of a given proposition. It is, however, 
convenient to have the two terms for these oppositions. 
Both are opposed to the given proposition, but the con- 
trary is harder to establish than the contradictory. 



102 THE ESSENTIALS OF LOGIC 

Conversion. Conversion is the process of inter- 
changing subject and predicate while the quality of 
the proposition remains the same. 4 No man is perfect ' 
becomes 'No perfect being is a man.' The original 
proposition is called the 4 convertend ' and the new one 
the ' converse.' 

We must not forget that in conversion we are deal- 
ing with propositions which have been reduced to logical 
form and that the relation stressed is that of the deno- 
tation of the class terms. This relation is mutual. The 
situation is analogous to the arithmetical relation of 
equality between two quantities. If A = B, then B « 
A. If S is contained in JP, P is to some extent con- 
tained in S. 

The rule of conversion is that no term may be dis- 
tributed in the converse which was not distributed in 
the convertend, The reason for this rule is obvious. A 
violation of it would involve making an assertion not 
justified by the denotation given in the original propo- 
sition. We should be going beyond our data. 

There are two kinds of conversion : (a) simple con- 
version ; (6) conversion by limitation, or per accidens. 
Simple conversion is the mere exchange of subject term 
and predicate term. E and I can be converted simply. 
Thus, ' No men are unaffected by self-interest ' becomes 
4 No individuals unaffected by self-interest are men.' 
Both terms are distributed in the converse, but they 
were already distributed in the convertend. Hence the 
rule is not violated. ' Some men are honest ' becomes 
' Some honest beings are men.' Both terms are undis- 
tributed in the first as in the second proposition. A 
must be converted by limitation. Thus, i All voters are 



THE IMPLICATIONS OF PROPOSITIONS 103 

citizens ' becomes ' Some citizens are voters.' In con- 
verting a universal affirmative, we are forced to pass 
from A to an L It will be remembered that the predi- 
cate of an affirmative proposition is undistributed. 

We have pointed out how E, A, and / can be con- 
verted. There remains O. But O cannot be converted 
because the result of an attempt would violate the rule. 
The undistributed subject term would become the predi- 
cate of a negative proposition and hence automatically 
claim distribution. The only way to interchange sub- 
ject and predicate in the case of an O proposition is to 
obvert first and then convert. This double process is 
called ' contraposition.' Before we pass to it, we must 
examine obversion. 

Obversion. Ohversion is the process of changing 
the quality of a proposition while retaining its mean- 
ing. We may wish to state an affirmative proposition 
in its corresponding negative form, or vice versa. When 
this is the case, we must obvert. Which form is first 
used depends upon the purpose and psychological setting. 
But it is often convenient to restate the proposition so 
as to bring out another emphasis. The mechanism of 
the syllogism, also, makes it preferable at times to 
change the quality. v --^ 

The method of obversion is to take the contradictory, 
or negative, of the predicate and then change the quality 
of the proposition. Its principle is that the denial of 
the contradictory of a predicate is the same as the affir- 
mation of the predicate, and the affirmation of the contra- 
dictory the same as the denial of the original predicate. 
No mistake must be made in taking the exact opposite, 
or contradictory, of the predicate. The contradictory of 



104 THE ESSENTIALS OF LOGIC 

a negative predicate gives, of course, a positive term. 
Let us take, first, the symbolic logical form, ' All /Sis P,' 
and obvert in order to show the mechanism of the proc- 
ess. P becomes not-_P, the quality is changed, and the 
proposition becomes ; No S is not-P.' The proposition 
i None of the crew were saved' becomes ' All of the crew 
were individuals who were not saved,' which, rendered 
into good English, is, 4 All of the crew perished.' 

The following examples may make this discussion of 
principle and method clearer : — 

A, 'All the people were rescued,' becomes, E, 'None of the 
people were lost.' 

E, 'No practical men are poets,' becomes, A, 'All practical men 
are not-poets.' 

/, ' Some vegetables are edible,' becomes, 0, ' Some vegetables 
are not inedible.' 

0, ' Some houses are not beautiful,' becomes, /, ' Some houses 
are ugly.' 

The student must be on his guard against two things : 
misinterpretation of the original proposition, the obver- 
tend, and the wrong treatment of the 
predicate. 

The principle of obversion can be 
represented graphically by means of a 
circle divided into two compartments. 
Fig. 7. (See fig. 7). 

" Then any given thing will fall into one or other 
of those compartments. If our proposition asserts that 
it falls into one, that is tantamount to asserting that it 
falls outside the other : the latter assertion would be 
the obverse of the former. S is P, implies that S is not 
not-P; T is not-P, implies that jTis not P."* 

1 Jones, Logic, Inductive and Deductive, p. 122. 





THE IMPLICATIONS OF PROPOSITIONS 105 

False Ob version. In valid ob version, the contradic- 
tory of the predicate is affirmed or denied, as the case 
may be, of the original subject. We have just noted the 
theory of such a change of quality. 
The universe is divided into P and 
not-P, and to affirm one is the same 
as to deny the other. This is the so- 
called 'law of counter-indication.' 
But this law does not hold of the 
subject in its relation to the predi- 

Fie* 8 

cate because the predicate is the 

larger term. If all S is P, it does not follow that 

no not-# is JP, as can be seen from the use of Euler's 

circles. 

An example of false obversion may make this situa- 
tion clearer. Take the proposition, ' All who are con- 
nected with this affair are honest.' Valid obversion 
would give, ' None who are connected with this affair 
are dishonest,' while false obversion would give, ' None 
who are not connected with this affair are honest.' It 
is obvious that the last proposition is not the equivalent 
of the other two. 

Contraposition. Contraposition is a process which 
combines obversion and conversion. Thus the quality 
of the proposition is changed and its terms are inter- 
changed. 4 No voters are aliens ' becomes by obversion, 
4 All voters are not-aliens (citizens),' and this, by con- 
version, becomes, 6 Some not-aliens (citizens) are voters.' 
No new principle is raised by contraposition. The prac- 
tical difficulty is to keep the first step clearly in mind 
while passing to the second. Inspection shows that the 
contrapositive has for its subject the contradictory of 



106 THE ESSENTIALS OF LOGIC 

the original predicate, while the quality is changed. 
This manipulation has value especially for the propo- 
sition. It will be remembered that an O statement 
cannot be converted because of the lack of distribution 
of the subject. By obversion becomes 7, and this can 
be converted simply. For example, ' Some men are not 
inventors ' becomes, successively, ' Some men are indi- 
viduals who are not inventors ' and 6 Some individuals 
who are not inventors are men.' 

Significance of Immediate Inference. The stu- 
dent can now better judge for himself the significance 
of immediate inference. Does he understand more com- 
pletely the meaning of propositions when he can work 
out their implications ? The processes are not hard to 
master and do repay attention. He who has mastered 
them does not have to guess whether one proposition is 
or is not equivalent to another. On the technical side, 
these processes are analogous to mental arithmetic, and, 
since they are always combined with the problem of 
reduction to logical form, give valuable discipline. The 
thinker must be in a position to handle propositions 
skillfully and correctly if he wishes to analyze and test 
his conclusions and those of others. 



REFERENCES 

Bode, An Outline of Logic, chap. v. 
Creighton, An Introductory Logic, chap. VII. 
Jones, Logic, Inductive and Deductive, chap. VII. 
Keynes, Formal Logic, chaps, ii, in, and iv. 



CHAPTER X 

THE SYLLOGISM AS A MECHANISM 

The Nature of the Syllogism. The syllogism was 
the discovery of Aristotle, that is, he was the first to 
work out its theory and its rules. His own definition 
should therefore serve very well to introduce us to a 
brief study of its nature. In the Prior Analytics, he 
offers the following broad one : " Discourse in which 
certain things being posited, something else than what 
is posited necessarily follows on their being true." To 
syllogize is to reason things together and draw a neces- 
sary conclusion. But when we examine the Aristotelian 
syllogism more closely and see it in its context, we real- 
ize that this definition is too broad. There is necessary 
reasoning which is not syllogistic. What, then, is the 
differentia? This is to be found in the character of the 
things posited. A syllogism is a discourse, or argu- 
ment, in which three propositions are so related that 
one of them (the conclusion^) follows from the other 
two. The germ of the invention was the analysis of 
propositions into terms. The syllogism was conceived 
by Aristotle as a reasoning together of terms. His 
prime discovery was that whenever two propositions 
necessarily contain or imply a conclusion they have a 
common term, that is, only three terms between them. 1 
In the last few chapters we have studied propositions 
separately, analyzing them, working out their implica- 

1 Minto, Logic, Inductive and Deductive, p. 170. 



108 THE ESSENTIALS OF LOGIC 

tions, reducing them to logical form. Now we must 
consider their interdependence. 

A single proposition taken by itself is an assertion 
which does not give its ground. When it is advanced 
by a person other than ourselves, we are almost sure 
to demand why this conclusion is reached rather than 
another. In other words, we want the assertion con- 
nected with some generally accepted principle as its 
consequence before we are inclined to give it assent. 
This backward movement to more basic propositions is 
characteristic of the syllogism, and gives us a clue to 
its purpose : it is an instrument of testing rather than 
an instrument of discovery. I would not say that it 
never leads to new conclusions, but it is primarily a 
method of determining the consistency of propositions 
already thrown out for acceptance. There has been 
much misunderstanding on this point both now and in 
the past. John Locke was protesting against the idea, 
commonly enough held in his day, that men should do 
their creative thinking in terms of the syllogism, when 
he made the oft-quoted gibe, " God has not been so 
sparing to men, to make them barely two-legged crea- 
tures, and left it to Aristotle to make them rational." 
Even to-day there are not wanting psychologists who 
are at great pains to demonstrate that the syllogism is 
not an adequate description of how reasoning actually 
takes place in human minds. But any argument should 
be capable of being thrown into the syllogistic form or 
something analogous to it for purposes of testing its 
validity and assumptions. If the conclusion follows nec- 
essarily from other propositions, the argument is valid 
or self -consistent. The conclusion need not, however, be 



THE SYLLOGISM AS A MECHANISM 109 

true. Only if the other propositions, from which it is a 
valid deduction, are true, is it true. 

Thus, the syllogism is an instrument which plays a 
part within a larger whole, that of experience and re- 
flection. When we come to study the logic of science, 
we shall better understand whence the propositions 
come which appear in the syllogism. The main point to 
realize now is that the syllogism cannot prove their 
truth and does not try to ; what it does try to prove, and 
can prove, is the consistency or inconsistency of their 
interrelations. 

An Analysis of the Syllogism. Having got a clear 
idea of the nature ' and work of the syllogism, we can 
now describe it. It is a very simple bit of mechanism 
resting on the analysis of propositions into their logical 
form as assertions or denials of relation between the 
denotation of classes. This relation to which attention 
is directed is that of inclusion and exclusion. It will be 
recalled that an A proposition is symbolized thus : ' All 
S is contained in P.' Now, Aristotle saw that two 
terms could be combined in a proposition as a result of 
their relation to a third term. The following typical 
syllogism will illustrate this simple underlying idea : — 

All men are mortal; 
Socrates is a man; 
Therefore Socrates is mortal. 

The three terms are, ' Socrates,' < mortal,' and 'man.' 
It is evident that ' Socrates ' and ' mortal,' the two 
terms brought together in the conclusion, are estab- 
lished in their relation by means of a third term to 
which both are related. What is the character of this 
relation which holds between these terms and makes 



110 THE ESSENTIALS OF LOGIC 

them into a system ? It is the relation of inclusion or 
exclusion, as the case may be, between their denota- 
tions. Applying Euler's circles to the above syllogism, 
we have — 




Pig. 9. 



Aristotle's idea comes out clearly enough in the so- 
called < Dictum de omni et nullo ' (statement concern- 
ing all and none) which is called the ' Axiom of the 
Syllogism.' " Whatever is predicated of All or None of 
a term is predicated of whatever is contained in that 
term." On the denotative side, this axiom is suffi- 
ciently expressed as follows : " A part of a part is a part 
of the whole." Thus, 4 all men ' is a part of i mortals ' 
and ' Socrates ' is a part of ' all men.' This is as much 
of an axiom as the corresponding one of geometry. 

The Elements of the Syllogism. We noted that 
Aristotle thought of the syllogism as a means of estab- 
lishing a relation, negative or positive, between two 
terms by reason of their relation to a common third 
term. This common third term necessarily appears in 
each of the premises, but does not appear in the con- 
clusion. The elements of the syllogism are, therefore, 
three terms and three propositions. The term common 
to the first two propositions is called the 4 middle term,' 
and these propositions are the ' premises.' The conclud- 



THE SYLLOGISM AS A MECHANISM 111 

ing proposition is the ' conclusion.' The other two terms, 
which appear in the conclusion, are the 4 extremes.' 
The subject of the conclusion, is called the 'minor 
term,' while its predicate is the 4 major term.' These 
are the extremes mediated by the middle term. The 
premise which contains the major term is the major 
premise and is usually stated first ; while the premise 
which contains the minor term is the minor premise. 

The conclusion is the moot point, the problem or the- 
sis in dispute. It is from it, therefore, that our thought 
starts. This fact shows that we are concerned in the 
syllogism with the mechanism of proof rather than with 
a movement of discovery. The question before our 
minds is, What premises will justify the conclusion? 
We are seeking the grounds of the conclusion. At this 
point we must note a certain difference in language 
form according as our thought moves downward to the 
conclusion from the premises or backward to the prem- 
ises from the conclusion. In the first case, we use such 
terms as ' therefore,' 6 hence,' etc. ; in the second case, 
such terms as ' because ' and ' since.' 

The major premise is, characteristically, the state- 
ment of some broad general principle, some generaliza- 
tion from experience which can be applied to particular 
instances. It serves both to interpret and support the 
conclusion. The minor premise, on the other hand, 
points to the specific application which is in question. 
It is, characteristically, more factual than the major 
premise. 

The Rules of the Syllogism. Having once com- 
prehended the mechanism of the syllogism and related 
it to the logical treatment of propositions as relations 



112 THE ESSENTIALS OF LOGIC 

of exclusion and inclusion between classes, it is easy to 
formulate and to prove certain rules which no valid 
syllogism can violate. They are as follows : — 

1. In every syllogism there should be three, and not 
more than three, terms, and these terms must be used 
throughout in the same sense. 

2. The middle term must be distributed at least 
once in the premises. 

3. No term ought to be distributed in the conclusion 
that was not distributed in the premises. 

4. No conclusion can be drawn from two negative 
premises. 

5. If one premise is negative, the conclusion must 
be negative. 

6. No conclusion can be drawn from two particular 
propositions. 

7. If one premise is particular, the conclusion must 
be particular. 

The first rule follows from the mechanism of the 
syllogism. It is founded, as we saw, on the recognition 
of a relation between the major and minor terms be- 
cause of their relation to a middle, or standard, term. 
The violation of this rule gives rise to the 6 Fallacy of 
Four Terms.' If the four terms were clearly distin- 
guishable, no one would try to syllogize them together. 
Thus, it would obviously be absurd to seek to draw a 
conclusion from such disparate propositions as, 'All 
men are mortal,' and ' Politics are improving in the 
United States.' But it sometimes happens that a term 
is ambiguous, there seem to be three when there are 
actually four terms. 

The second rule brings out the condition without 



THE SYLLOGISM AS A MECHANISM 113 

which the middle term cannot perform its assigned 
function. Were both the major and the minor terms 
related to only a part of the middle term, we could 




Fig. 10. 

have no assurance that they were related to the same 
part. In other words, the information given would not 
tell us about the relative position of the terms to ap- 
pear in the conclusion. This indefiniteness reveals itself 
in the relations of the circles representing the three 
terms. If in accordance with tradition, we let S, P, 
and M stand for minor, major, and middle term respec- 
tively, an undistributed middle shows itself in the exist- 
ence of different possibilities. (Fig. 10.) 

This is illustrated more concretely in the following 

argument : — 

All voters are citizens; 
These men are citizens; 
Therefore these men are voters. 

Diagrammatically, this syllogism is unsettled. We 
are not able to determine a fixed relative position for 
the two classes, these men and voters. (Fig. 11.) 

A breach of this second rule involves the fallacy 
known as « Undistributed Middle.' 



114 



THE ESSENTIALS OF LOGIC 



The basis for the third rule is the very nature of the 
conclusion as a logical sequence from the premises. We 
have no right to say more about a term in the conclu- 
sion than was said in its premise. This principle has 
already appeared in ' Immediate Inference ' in conver- 
sion. A violation of the third rule in connection 
with the major term is called c Illicit Process of the 
Major,' or, more briefly, ' illicit major ' ; its violation 
in connection with the minor term, ' Illicit Process of 
the Minor,' or i illicit minor.' One example may serve 

for both. 

All good citizens are voters; 
This person is not a good citizen; 
Therefore this person is not a voter. 

The conclusion is a singular proposition and nega- 
tive. It will be remembered that the predicate of a 

negative proposition is distrib- 
uted. But this term is not dis* 
tributed in the major premise. 
Hence this is a case of illicit 
major. This fallacy may be il- 
lustrated by circles. 

The fourth rule is understood 
as soon as we realize that two 
negative premises mean that 
there is no term by means of which we can locate the 
major and minor with reference to each other. Func- 
tionally, there is no middle, or mediating, term. We 
know that 8 and P both fall outside of Jf, but that 
fact gives us no clue in regard to their interrelation. 
This lack of mediation appears in the following argu- 
ment : — 




rig. 11. 



THE SYLLOGISM AS A MECHANISM 115 

No bird is a bat; 
This is not a bird; 
Therefore this is a bat. 

The use of circles may make the situation clearer. 

I Birds I (creature) I Bats J 

Fig. 12. 

What the rule points to is our inability to draw a 
conclusion from the information given in the premises. 
This may be a bat, but there are other possibilities. 
In applying this rule, we must be on our guard against 
propositions which are only apparently negative. Care 
in the analysis of sentences must precede the use of 
these formal rules. 

The fifth rule is seen to hold as soon as we note that 
the two terms related in the conclusion do not have the 
same relation to the middle term. If one premise is 
negative, one of the extremes must be excluded in 
whole or in part from the middle term. But the other 
premise must be affirmative by rule four, and therefore 
asserts a partial or total inclusion in the middle term. 
This alliance with a term which excludes the other ex- 
treme involves it also as a party to the exclusion. 

The sixth rule can be demonstrated by means of the 
preceding rules. Both premises cannot be particular 
and contain the necessary distribution. In the first 
place, only one of the two particulars can be negative 
(rule 4). There are left three possibilities, /_/", / 0, 
and 01 II fails because it does not distribute the 



116 THE ESSENTIALS OF LOGIC 

middle term. / and I fail for another reason ; 
they involve a negative conclusion (rule 5). But a 
negative conclusion means that the major term must 
be distributed in the major premise. But neither I 
nor / can distribute more than one term. Hence 
an argument having two particular premises is invalid 
because it commits either the fallacy of undistributed 
middle or that of illicit major. 

The seventh and last rule can be demonstrated in 
much ,the same way as the sixth. If one premise be 
particular, there are three general possibilities, a com- 
bination of A and I, of A and 0, and of E and L If 
A and / have a universal conclusion, the minor term, 
the subject of the conclusion, must be distributed in the 
minor premise to avoid an illicit minor. But the pre- 
mises together distribute only one term, and this must 
be the middle (rule 2). Bearing in mind the distri- 
bution of the terms in the four kinds of propositions, 
the student can easily prove why A O and E I cannot 
have universal conclusions. 

The Formal Syllogism and Actual Reasoning. 
In the present chapter, we have treated the syllogism 
as a mechanism for testing the consistency of an argu- 
ment. While such knowledge as we have gained is 
useful, there are vital objections to this purely formal 
view. In the first place, if the major premise is known 
to be true, the instance subsumed must already be 
known. We cannot know that all men are mortal 
without feeling that Socrates is mortal. There is no 
real advance in thought from the major through the 
minor to the conclusion. To this criticism of the syl- 
logism, it is usually replied that the major premise is 



THE SYLLOGISM AS A MECHANISM 117 

really the statement of a rule which we take to be with- 
out exceptions^ and the minor is the statement of an 
instance. If so, there is always a hazard in the syllo- 
gism, a point which we shall understand better when 
we come to the actual movement of scientific thinking. 
Another objection to the syllogism concerns the middle 
term. In an actual argument, how can you be certain 
that you have an unambiguous middle term ? Take the 
following example : — 

All men love good stories; 
Smith is a man; 
Therefore Smith loves this good story. 

" Smith is in general a 4 man,' and, therefore, loves 
good stories, but he is not a i man ' for the purpose of 
this particular conclusion ; and so the sense of * man ' 
in the two premises is not the same, and this vitiates 
the argument." 1 This example brings out the fact that 
it is not always easy to apply a rule or, conversely, to 
know when an instance comes under a rule. Differ- 
ences may be very important. 

In actual reasoning, induction and deduction march 
together. Our knowledge of general principles develops 
as we apply them. There is an interpretation of rules 
by new facts and, at the same time, a reading of facts 
in terms of rules. 



REFERENCES 

Creighton, An Introductory Logic, chap. vni. 
Jones, Logic, Inductive and Deductive, chap. virr. 
Minto, Logic, Inductive and Deductive, part IV, chap. I. 
Schiller, Formal Logic, chap. xvi. 

1 Schiller, Formal Logic, p. 200. 



CHAPTER XI 

THE FIGURES AND MOODS OF THE SYLLOGISM 

The Figures of the Syllogism. The ' figure ' of a 
syllogism is determined by the position of the middle 
term. Since the middle term may be subject or predi- 
cate in each of the two premises, four arrangements or 
figures are possible. Using the conventional symbols, 
we may state these four figures as follows : — 

1. M is P 2. P is M 3. M is P 4. P is M 

SisM SisM MisS MisS 

S is P SisP S is P S is P 

Inspecting these arrangements of the three terms in 
the two premises, we find that the middle term is the 
subject of the major premise and the predicate of the 
minor in the first figure. This figure was considered by 
Aristotle the most satisfactory and was therefore called 
the perfect figure. The middle term is contained in the 
major, and the minor in the middle term. 

In the second figure, the middle term is the predicate 
of both premises. 

In the third figure, it is the subject of both predi- 
cates. 

In the fourth figure, it is the predicate of the major 
premise and the subject of the minor premise. 

The Moods of the Syllogism. The ' mood ' of a 
syllogism depends upon the quality and quantity of the 
propositions composing it. It will be remembered that 
there are four kinds of propositions symbolized by the 



FIGURES AND MOODS OF THE SYLLOGISM 119 

letters J., E, I, and 0. If we leave out all question o£ 
validity, these letters may be combined in threes to 
make the possible moods of the syllogism. The sixty- 
four possible moods thus obtained are as follows : — 

AAA ArE-A: A-^A- Ar-O-A- EAA E-E-A- EI A E-G^A 

AAE AEE A IE AOE EAE EEE E I E EOE 

AA I AE-*- A I I ArO-t &A4- -frE-t E-t-4- -E-O-i- 

AAO AEO A I AOO EAO EEO EIO EOO - 

^rAr 3-E"Ar H-A- *-OtA- OAA OEA OIA O O A - 

^AdE- I-EE- 4-H3- I OE OAE OEE IE OOE 

I A I *-E-I- HHE- i-e-t -O^-I- OE I O I I 00 I - 

*-ArO- (I E.O) -Hfc-G- *-frO- OAO OEO 010 00 - 

Fig. 13. 

Many of these mathematically possible moods are soon 
seen to be invalid. Thus, by applying rules 4 and 5, 
that no conclusion can be drawn from two negative or 
two particular premises, we can decide on the invalidity 
of those moods through which a line is drawn. I E O 
must also be discarded because it sins against rule 3 ; 
it is clearly a case of illicit major. We are left with 
eleven moods, some of which are valid in certain of the 
four figures and invalid in others. The reason for this 
variation in validity according to figure is the relation 
between distribution and the position of the terms. We 
must now ask ourselves what moods are valid in the 
first, second, third, and fourth figures respectively. 

There are two ways of determining the valid moods 
of each figure : by inspection and by the establishment 
of special rules for each figure. We shall use both 
methods for the first figure and then only state the 



wo 



THE ESSENTIALS OF LOGIC 



special rules for the other figures, leaving it to the 
student to demonstrate them. 

Taking the eleven moods which were left us after the 
first general elimination and arranging the terms in 
accordance with the first figure, we have the following 
results : — 



A. All 2His P 
A. All 51s M 
A. All S is P 



A. All M is P 
A. All 5 is M 
I. Some £ is P 




A. A113fisP 
I. Some S is Mi 
L Some 5 is P 




. E. No M is P 

lot P A. All S is M 

t P - JE7. No 5 is P 



JSJ. NoikTisP 
I. Some S> is M 
0. Some 5 is not P 






JE7. NoilfisP 

^.. All S is M 

P : 0. Some £ is not P 
Fig. 14. 

Applying to these possible moods of the first figure 
the general rules of the syllogism, we soon discover that 
A EE, AE O, A 0, I A I, and O A O are in- 
valid because of an undistributed middle or an illicit 
major. Crossing these out, we have AAA, A A I, 
All, EAE,EA O, and EIO left as valid. Of 
these A A /and E A are the same as A A A and 
E A E in the premises and have weakened conclusions ; 
they have therefore no essential independent value. 



FIGURES AND MOODS OF THE SYLLOGISM 121 

This analysis of the possible moods of the first figure 
should illustrate the use made of distribution in the 
syllogism. An inspection of the valid moods leads to the 
discovery of the two following special rules for the first 
figure : — 

1. The minor premise must be affirmative. 

2. The major premise must be universal. 

These two rules can also be demonstrated by means 
of the general rules of the syllogism. To prove that the 
minor premise must be affirmative, we use the indirect 
method of approach. Suppose it to be negative ; then 
the conclusion must be negative (rule 5). But if the 
conclusion is negative, the major term must be dis- 
tributed (rule 3). To distribute P, the major premise 
must be negative since only the predicates of negative 
propositions are distributed. But by hypothesis, the 
minor premise is already negative. Hence we should 
have two negative premises, which is impossible. It fol- 
lows that the minor premise must be affirmative. 

Having established this rule, we can easily show that 
the major premise must be universal. An affirmative 
minor does not distribute the middle term in the first 
figure. Hence it must be distributed in the major prem- 
ise (rule 2). But only a universal will do this. Thus 
the second special rule follows. 

A similar method is applicable to the three other 
figures. For the sake of completeness, the special rules 
for these figures will be given. There is no need to bur- 
den the memory with them, however, as in actual prac- 
tice the general rules will be found sufficient as tests of 
validity. 

The rules for the second figure are : — 



122 THE ESSENTIALS OF LOGIC 

1. The conclusion must be negative, and one premise 
must, also, be negative. 

2. The major premise must be universal. 

For the third figure they are : — 

1. The conclusion must be particular. 

2. The minor premise must be affirmative. 

For the fourth they are as follows : — 

1. If either premise be negative, the major premise 
must be universal. 

2. If the major premise be affirmative, the minor 

must be universal. 

3. If the minor premise be affirmative, the conclu- 
sion must be particular. 

Reduction to the First Figure. We noted that 
Aristotle regarded the first as the perfect figure. He 
did so because the Axiom of the Syllogism has in it 
its simplest application. On the propositional side, the 
minor premise is subsumed under the major, which is a 
universal. The process of changing the other figures to 
the valid moods of the first is called * reduction.' Dur- 
ing the Middle Ages, when the syllogism held such a 
revered place, elaborate rules for this reduction were 
worked out and embodied in mnemonic lines. This pro- 
cess and these lines have had such a place in history 
that it would seem unwise not to mention them. There 
is an inimitable flavor of the past about them. Reduc- 
tion is, moreover, a process which casts light upon the 
mechanism of the syllogism and connects it with con- 
version. 

The following verses in scholastic Latin served the 



FIGURES AND MOODS OF THE SYLLOGISM 123 

double function of recalling the valid moods of each 
figure and of giving rules for reduction : — 

Barbara, Celarent, Dam, Yerioqxie prioris ; 
Cesare, Camestres, Yestino, Baroko, secundaB ; 
Tertia, Darapti, Disamis, Datisis, Yelapton, 
Bokardo, Yerison, habet; quarta insuper addit 
Bramantip, Camenes, Dimaris, Yesapo, Yresison. 

Unless one has a very facile memory, there is not 
sufficient value in the stanza to justify memorizing. It 
is interesting to see its construction and to realize how 
it was used. The vowels in the names give the moods. 
Thus, ' Barbara ' is the AAA mood of the first figure. 
The words in genuine Latin indicate the figures. Sup- 
pose we select ' Disamis ' in the third line. Since it is 
in the third figure we must write it in logical symbols 
as follows : — 

/. Some If is P. 

4- All M is £. 

/. Therefore some S is P. 

The first letter of each mood of the ' imperfect ' fig- 
ures indicates the corresponding valid mood of the first 
figure to which it can be reduced. Thus, * Cesare ' and 
4 Camestres' of the second figure are reducible to 
4 Celarent ' of the first. The letters s, m, and p also have 
their meaning for the process of reduction. Placed after 
a vowel, s indicates that the proposition represented by 
the vowel must be converted simply ; m (muta) indicates 
that the premises must be interchanged; while p shows 
that the proposition after which it is placed must be con- 
verted by limitation, or per accidens. An example of 
reduction will make this clearer. Take 4 Disamis ' again. 
The initial letter indicates that i Darii ' is the corre- 



124 THE ESSENTIALS OF LOGIC 

sponding mood of the first figure. I A I oi the third 
figure becomes A I Ioi the first by conversion of the 
major premise, interchange of the premises, and, finally, 
conversion of the conclusion to correspond to the trans- 
formation of the major term into a minor. 

Comparative Value of the Figures. While the 
tradition in logic has favored the view that the first 
figure is somehow better than the others, a closer anal- 
ysis has shown that they are independently valid and 
do not need reduction. They are independent types. 
In other words, the Axiom of the Syllogism holds 
primarily of the first figure and does not apply directly 
to the others. Different classes of arguments naturally 
fall into different forms. Thus, arguments involving the 
subsumption of an instance under a general principle 
take the first figure ; while those drawing negative con- 
clusions from the absence of distinctive signs take the 
second. The following example of a second-figure syl- 
logism will bring out this difference : — 

All fever-stricken patients are thirsty. 
This patient is not thirsty. 
He is not fever-stricken. 1 

A close inspection of this argument reveals the realiza- 
tion that if thirstiness is taken as a sign of fever, its 
absence is necessarily a sign of the lack of fever. It is 
for this reason that Minto speaks of the second as the 
* Figure of Negative Diagnosis/ The third and fourth 
figures are of little value. It should be remembered 
that the third can give only a particular conclusion. 
For this reason it has sometimes been called the 

1 Minto, Logic* 



FIGURES AND MOODS OF THE SYLLOGISM 125 

'Inductive Figure.' The fourth is more of a tour de 
force and is not always admitted. Arguments do not 
naturally fall into it. 



REFERENCES 

Creighton, An Introductory Logic, chap. ix. 
Hibben, Logic, Deductive and Inductive, part I, chap. XVI. 
Jones, Logic, Inductive and Deductive, chap. IX. 
Minto, Logic, Inductive and Deductive, bk. i, part IV, chaps. II 
and in. 



CHAPTER XII 

ABBREVIATED AND EXPANDED ARGUMENTS — EXTRA- 
SYLLOGISTIC ARGUMENTS 

Enthymeme. It is seldom that all the parts of an 
argument are stated fully and explicitly. Some premise 
is taken for granted or is considered too obvious to 
justify formal statement. The thinker himself has not 
taken the time to analyze and formulate the grounds 
for his conclusion or he feels that his listeners wish 
only the salient points and can supply the remainder. 
In the first case, what he says reflects what has been up- 
permost in his mind ; in the second case, he wishes to 
state only the necessary in order not to be wooden and 
pedantic. All this is natural and there is nothing in it 
which the logician has the right to condemn. Neverthe- 
less, such condensation has its dangers against which 
the logician must issue his warning. Oftentimes sup- 
pressed premises are debatable and pass just because 
attention has not been called to them. They slink by, 
as it were, because they wear caps of darkness which 
hide their faces from scrutiny. 

The logician does not wish to be the enemy of wit, 
but he can never forget that he is the guardian of rea- 
son. Brevity is the soul of wit and of the epigram, yet 
such syncopation must be capable of valid enlarge- 
ment. It is of the character of such enlargement that 
the syllogism informs us. When a premise or the con- 
clusion of an argument is not stated, the argument 
has the form of an enthymeme. The reasoning is not 



ABBREVIATED ARGUMENTS 127 

fully expressed. An enthymeme is, in brief, an ellip- 
tical argument. A few examples will make this clear: — 

4 Death cannot be an evil, being ^universal.' * 

4 He is in love. He brushes his hat.' 2 

4 She is a woman, therefore may be won.' 3 

Carlyle says of Sansculottism : 4 It too came from 
God ; for has it not been ? ' 

It will be seen from these examples that literature is 
full of enthymemes. They add to the charm of a writer 
if not used too lavishly. On the other hand, they do 
not have so assured a place in arguments of a more di- 
dactic character as in science and philosophy. Not to 
leave things obscure is a merit in these fields. 

Enthymemes are of the first, second, or third order 
according as the major premise, the minor premise, or 
the conclusion is wanting. The absence of the conclu- 
sion is a rhetorical device to make it more emphatic. 

It is usually quite easy to supply the missing part 
of the argument. The two propositions which are given 
contain the three terms. Hence all that is needed is 
the perception of what proposition is absent and its 
construction. Thus the quotation from Goethe given 
above becomes — 

Whatever is universal is not an evil; 
Death is universal ; 
Death is not an evil. 

Frosyllogisms and Episyllogisms. Either prem- 
ise of a syllogism may be justified by making it the 
conclusion of another syllogism. When this is done, the 
result is a complex argument in which one syllogism 
prepares the way for a second. The grounds of one of 

1 Goethe. 2 Much Ado About Nothing. 3 Titus Andronicus. 



Prosyllogism 



Episyllogism 



128 THE ESSENTIALS OF LOGIC 

the premises of the final conclusion are offered. The first 
syllogism in such a complex is called the ' prosyllogism/ 
and the last the 'episyllogism.' Any connected argu- 
ment of length involves the existence of interrelated 
syllogisms. The following is a good example : — 

'Everything which is able to restrain trade is a 

source of danger ; 
Every monopoly is able to restrain trade ; 
Hence, every monopoly is a source of danger. 
" A company which has a complete control of a 

certain commodity is a monopoly ; 
This trust has complete control of a certain 

commodity ; 
Hence, this trust is a monopoly. 

Final Conclusion. This trust is a source of danger. 1 

It will be noted that the conclusions of the first two 
syllogisms are the premises of the final conclusion. 

Sorites. When many syllogisms are combined, as 
above, the combination is called a ' polysyllogism.' When 
all the intermediate conclusions are suppressed, a poly- 
syllogism becomes a ' sorites.' A sorites is a chain or, 
literally, a piling-up of premises leading to a conclusion. 
The argument gathers weight as it proceeds. 

Two types of sorites have been distinguished, the 
'Progressive' or 'Aristotelian,' and the 'Regressive' 
or 'Goclenian.' The Aristotelian sorites moves from 
the least inclusive term to the most inclusive, from the 
subject of the conclusion to the predicate. 

A is B. All Frenchmen are Europeans ; 
B is C, All Europeans are men ; 
C is D. All men are animals ; 
D is E. All animals are mortal ; 
A is E. All Frenchmen are mortal. 

1 Jones, Logic, Inductive and Deductive. 



EXTRA-SYLLOGISTIC ARGUMENTS 129 

The Goclenian sorites moves in the opposite direc- 
tion. 

D is E. All animals are mortal ; 

C is Z). All men are animals ; 

B is C. All Europeans are men ; 

A is B. All Frenchmen are Europeans ; 

A is E. All Frenchmen are mortal. 

A sorites can be expanded into a polysyllogism of 
which each unit is a syllogism of the first figure. In- 
spection will show the student that the order of each 
pair of premises must be changed to accomplish this ex- 
pansion. 

The following example of the use of the sorites in 
poetry is worth quoting to show how a logical form may 
be clothed upon and become a thing of beauty : — 

The longer life the more offence, 
The more offence the greater paine, 
The greater paine the lesse defence, 
The less defence the lesser gaine ; 
The loss of gaine long yll doth trye, 
Wherefore come death and let mee dye. 

Come gentle Death, the ebbe of care, 
The ebbe of care the flood of life, 
The flood of life the joyf ull fare, 
The joyf ull fare the end of strife, 
The end of strife that thing wish I ; 
Wherefore come death and let mee dye. 1 

Extra-Syllogistic Arguments. Not all forms of 
reasoning are syllogistic in type. For example, 'A^B, 
B = (7 .-. A = C.' We all recognize the cogency of this 
reasoning, yet we have no tendency to reduce it to syl- 
logistic form. Instead, it is perceived to be an instance 
of an axiom which appeals to us as undeniable, namely, 

1 Sir Thomas Wyatt, 1503-44. 



130 THE ESSENTIALS OF LOGIC 

things which are equal to the same thing are equal to 
each other. The argument is in accord with the axiom, 
yet the axiom does not appear as a major premise in it. 
Deny the axiom, and you would be forced to reject the 
instance ; but it is possible to accept the instance and 
seal its cogency without formulating the axiom. 1 

At one time there was a tendency to interpret such an 
argument as really syllogistic, as an enthymeme with an 
unformulated major premise, and to complete it thus : — 

Things equal to the same thing are equal to each other ; 
A and C are things equal to the same thing ; 
A and C are equal to each other. 

But inspection shows that our minor premise is not 
an exact reproduction of the original argument, which 
was that A and C are both equal to B. Even with this 
correction, we are not over our difficulties, for ' A and 
<7,' the apparent minor term, is not a term at all but 
two objects. 

The truth is, that the syllogism is limited to the re- 
lations between classes in the way of inclusion and ex- 
clusion. So far as there is an axiom involved, such as 
the dictum de omni et nullo, this axiom is no more a 
major premise than the axiom, that things equal to the 
same thing are equal to each other, is an implied ma- 
jor premise for the mathematical argument referred to 
above. Deny either axiom, and, of course, the particu- 
lar arguments fall to the ground. An examination of 
other types of arguments may make the situation clearer 
and enable us to realize that in the syllogism we are 
dealing with a comparatively simple sort of relation be- 
tween classes. The point is, that in extra-syllogistic 

^See Joseph, An Introduction to Logic, p. 273. 



EXTRA-SYLLOGISTIC ARGUMENTS 131 

reasoning we have to do with different systems of re- 
lation, some of which are definite and some of which 
are indefinite. Only when the system is well enough 
known to justify a conclusion can we move freely 
within it. 

Quantitative Relations 

A is greater than B) 

B is greater than C V Conclusion valid 

A is greater than C) 

Relations of Direction 

A is north of B\ 

B is north of C f Conclusion valid 

A is north of C) 

In these cases, we move within a unitary system and 
can travel, as it were, back and forth in it. Each sys- 
tem has an axiom, but the axiom is founded on some- 
thing of the nature of immediate perception. In the 
following instance the absence of such a unitary field 
of relations between things is immediately recognized : — 

A is the employer of B\ 

B is the employer of C Y Conclusion invalid 

A is the employer of C) 

The study of extra-syllogistic reasoning is valuable 
because it brings into relief the character of the syllo- 
gism. It enables us to see that the subject-matter 
is fundamentally important. 

REFERENCES 

Bode, An Outline of Logic, chap. VI. 
Creighton, An Introductory Logic, chap. x. 
Bradley, The Principles of Logic, pp. 348-60. 
Joseph, An Introduction to Logic, chaps, xvi and xvii. 



CHAPTER XIII 

HYPOTHETICAL AND DISJUNCTIVE SYLLOGISMS 

In a very real sense all propositions are categorical, 
for they all make assertions. But it has been customary 
for logic to distinguish propositions in which a predicate 
is directly asserted of a subject from two other forms 
of assertion, the hypothetical and the disjunctive. It will 
be remembered that these propositional forms were 
briefly defined in a previous chapter. They are of 
interest to us now because they appear as the major 
premises of two other kinds of syllogisms called, respec- 
tively, the ' hypothetical ' and the 4 disjunctive.' 

The Hypothetical Syllogism. A hypothetical 
proposition combines a condition with a consequent. 
4 If this, then this,' is the general form. Thus, * If it 
rains this afternoon, I shall not go out for a walk,' and 
* If business is good, I shall buy an auto,' are examples 
of this form of assertion in which an antecedent is re- 
lated to an inevitable consequent. A little reflection 
shows how extensive is this expression of a relation be- 
tween two events. It is not too much to say that modern 
science is chiefly concerned with the discovery of rela- 
tions. In practical life, again, we wish to know what to 
do in order to secure certain desirable results. If we can 
once find a rule, we have only to apply it. 

In a hypothetical syllogism, the major premise is 
hypothetical, while the minor is categorical. The cate- 
gorical minor either affirms the antecedent or denies 



HYPOTHETICAL SYLLOGISMS 133 

the consequent of the major premise. When it affirms 
the antecedent, the syllogism is said to be ' constructive,' 
or in the modus ponens; when it denies the consequent, 
the syllogism is ; destructive,' or in the modus tollens. 
An example of each type may make this distinction 
clearer : — 

If the winter is really over, we shall have some warm weather ; 

The winter is really over ; 

Therefore we shall have some warm weather. 

This argument is constructive because we affirm the 
antecedent and thereby have the right to affirm the 
consequent in the conclusion. In the following, how- 
ever, we deny the consequent : — 

If human life were considered precious, war would be judged 
a crime ; 
War is not judged a crime ; 
Therefore human life is not considered precious. 

It should be noted that the distinction between affirm- 
ative and negative has no meaning for hypothetical 
propositions. We are either able to affirm a connection 
between an antecedent and a consequent or we are not 
able so to do. In the latter case we are not able to pass 
any judgment of this character. The most we can do is 
to state a probability. In a later chapter we shall study 
the nature of probability ; but it would complicate things 
too greatly to introduce it here. 

Another point needs attention. Either the anteced- 
ent or the consequent or both may be negative. In such 
a case the categorical minor may be negative in form and 
yet affirm the antecedent, or affirmative in form and 
yet deny the consequent. The way to avoid error is to 
get both parts of the major premise clearly before the 



134 THE ESSENTIALS OF LOGIC 

mind, and then to see them in their relation to the minor. 
In the following syllogism the minor is negative in form, 
yet it affirms the antecedent : — 

If there is not a strike at the works, the union has been dis- 
rupted ; 

There is not a strike at the works ; 
Therefore the union has been disrupted. 

The Rule of the Hypothetical Syllogism. The 

rule of the hypothetical syllogism is sometimes spoken 
of as the ' Law of Reason and Consequent.' It is for- 
mulated thus: The truth of the consequent follows from 
the truth of the antecedent, and the falsehood of the an- 
tecedent from the falsehood of the consequent. This law 
expresses the nature of the necessary relation affirmed 
to exist between them. 

The Fallacies of the Hypothetical Syllogism. 
To attempt to draw a conclusion by denying the anteced- 
ent or by affirming the consequent gives rise to error. 
The reason for this is apparent so soon as we realize that 
one event may have more than one antecedent. If we 
have information that tells us that B occurs only when 
A occurs, we are able to build up four valid hypotheti- 
cal syllogisms : — 

If A, then B ; A is; therefore B is. 

If A , then B ; A is not ; therefore B is not. 

If A, then B ; B is ; therefore A is. 

If A, then B ; B is not ; therefore A is not. 

In such a case, we are able to move in both direc- 
tions because B's existence is bound up only with A's. 
But ordinarily this is not the case. Hence B may exist 
even when A does not. An example may make this 
clearer : — 



HYPOTHETICAL SYLLOGISMS 135 

If the harbor is frozen, the ships cannot come in ; 
The harbor is not frozen ; 

Can we draw a conclusion in this case ? No ; because 
there may be other reasons why the ships cannot come 
in. The harbor may be mined, or there may be a storm. 

Reduction to Categorical Form. It has been 
customary to reduce hypothetical syllogisms to the cate- 
gorical form and to find analogies therein for these two 
fallacies. But to reduce the simple to the complex is 
wasted effort, and there is little doubt that much of our 
thinking falls naturally into the hypothetical form. It 
would seem more reasonable to reduce categorical syllo- 
gisms to this simpler form. For the sake of completeness, 
I shall perform both reductions. 

If war is not declared, our country will escape disaster; 

But war will not be declared; 

Therefore our country will escape disaster. 

Eeduced to categorical form, this becomes: — 

All cases of war not being declared are cases of our country 
escaping disaster; 

This is a case of war not being declared; 

Therefore this is a case of our country escaping disaster. 

It will be noted that a relation of events is changed 
into an inclusion of classes. As a matter of fact, the 
major premise of a categorical syllogism usually states 
a principle, and the minor premise an instance. Its 
meaning is often more clearly expressed as a hypo- 
thetical. 

All men are mortal; 
Socrates is a man; 
Therefore Socrates is mortal. 

really means : — 



136 THE ESSENTIALS OF LOGIC 

If man, then mortal; 
Socrates is a man ; 
Therefore Socrates is mortal. 

8 All men are mortal ' is not an enumerative proposi- 
tion, but the statement of a relation between man's 
nature and his mortality. If it were enumerative, we 
should already know that Socrates was mortal. The 
logician must be the first to recognize that language 
forms are often accidental. 

The Disjunctive Syllogism. In a disjunctive syl- 
logism, the major premise is disjunctive, while the 
minor is categorical. Thus, the major premise expresses 
alternative possibilities among which the minor makes 
a selection. ' The inventor of the calculus was either 
Leibnitz or Newton,' and 6 That bird was either a sand 
martin or a swallow,' are typical disjunctives. The 
minor premise either asserts or denies one of the alter- 
natives. The conclusion either denies or asserts the 
other. For example : — 

This man is either very clever or a cheat; 
He is not very clever; 
Therefore he is a cheat. 

The source of danger is in the major premise. The 
alternatives there offered must be exclusive of each 
other. Unless this is the case, the affirmation of one of 
them does not enable us to make an assured statement. 
Hence, we may say that the ideal form of disjunction 
is that between contradictories. ' Sempronius is either 
honest or dishonest,' 'This man acquired his wealth 
worthily or by fraud,' 4 He was either married or un- 
married ' are examples of clear-cut exclusion. On the 
other hand, a man may be both a knave and a fool. If 



DISJUNCTIVE SYLLOGISMS 137 

so, the assertion that he is a fool does not enable us to 
proclaim that he is not a knave. Again, it is only too 
common to assume that a man must be moved either 
by self-interest or by altruism, whereas motives are 
nearly always mixed. Great care must be taken in for- 
mulating the major premise of a disjunctive syllogism. 

The Dilemma, A dilemma is technically defined 
as an argument in which the major premise is a com- 
plex hypothetical proposition and the minor is disjunc- 
tive. Practically, it means the presentation of two or 
more alternatives, all of which are unpleasant. 

A dilemma may be constructive or destructive, sim- 
ple or complex. If the antecedents of the hypothetical 
major are affirmed in the minor premise, the dilemma 
is said to be ' constructive ' ; if the consequents are 
denied, it is * destructive.' Thus the rule at work is the 
Law of Eeason and Consequent. The new element is 
the disjunctive minor. A dilemma is simple when the 
consequents are the same for both antecedents; com- 
plex, when the consequents of the hypothetical major 
are not the same for both antecedents. 

The following is an example of a simple constructive 
dilemma : — 

If A is B, C is D; and if E is F, C is D; 
But either A is B or E is F; 
Therefore C is D. 

If a man acts in accordance with his own judgment, he will be 
criticized ; and if he is guided by the opinions and rules of others, 
he will be criticized; 

But he must either act in accordance with his own judgment, 
or be guided by the opinions of others ; 

Therefore, in any case, he will be criticized. 1 

1 Creighton, An Introductory Logic* 



138 THE ESSENTIALS OF LOGIC 

The structure of the complex constructive dilemma 
is exemplified in this argument : — 

If a statesman who sees his former opinions to be wrong does 
not alter his course he is guilty of deceit; and if he does alter his 
course he is open to a charge of inconsistency; 

But either he does not alter his course or he does; 

Therefore, he is either guilty of deceit, or he is open to a charge 
of inconsistency. 

It should be noted that the conclusion of this argu- 
ment is disjunctive. The following is an oft-quoted 
complex destructive dilemma : — 

If this man were wise he would not speak irreverently of the 
Scripture in jest; and if he were good he would not do it in ear- 
nest; 

But he does it either in jest or in earnest; 

Therefore he is either not wise or not good. 

There are three ways of meeting a dilemma, all of 
which have picturesque names. One may try to escape 
between the horns of a dilemma, these being the alter- 
natives on which you are to be impaled. To escape is 
to show that there is some other alternative. One may 
try to rebut a dilemma by constructing another with a 
contradictory conclusion. Or, finally, one may try to 
take a dilemma by the horns by accepting an alterna- 
tive and proving that the consequence asserted does not 
follow. 

Since it is difficult to get an exhaustive disjunction 
for the minor premise, it is usually easiest to escape 
between the horns. The rebuttal of a dilemma is an in- 
teresting process, and many examples have come down 
to us from antiquity, chief of which is the story of Pro- 
tagoras and Euathlus. This story, called Litigiosus, is 
as follows : — 



DISJUNCTIVE SYLLOGISMS 139 

Protagoras had agreed with Euathlus to teach him 
rhetoric for a fee, of which half was to be paid at the 
conclusion of the instruction, and the remainder when 
Euathlus won his first suit in court. Observing that 
the latter delayed to practice, Protagoras thought he 
was endeavoring to evade payment, and therefore him- 
self brought a suit for the recovery of the second half 
of his fee. He then argued with the jury that Euathlus 
ought to pay him, in the following way : — 

If Euathlus loses this case, he ought to pay by the judgment 
of the court; and if he wins it, he ought to pay by his own agree- 
ment; 

But he must either lose it or win it; 

Therefore he ought to pay. 

Euathlus rebutted this dilemma by a counter-dilem- 
ma: — 

If I win this case, I ought not to pay by the judgment of the 
court; and if I lose it, I ought not to pay by my own agreement; 
But I must either win or lose it; 
Therefore I ought not to pay. 

An examination of these two dilemmas shows that 
each antecedent has two consequents, one only of which 
is used in each dilemma. There are, in other words, 
two standards and each disputant uses them only when 
convenient. This conflict of standards must first be set- 
tled before the problem can be cleared. Has Protagoras 
ground for action ? He could sue him only for refusing 
to plead. But is there evidence that Euathlus had 
agreed to become a pleader ? 

The dilemma is a controversial instrument. When 
validly constructed, it is very effective. But it is an 
instrument which may be turned against the user and 



140 THE ESSENTIALS OF LOGIC 

then becomes a trap in which the hunter is himself 
taken. Before resorting to the dilemma, one should be 
certain that the situation is itself dilemmatic. 



REFERENCES 

Creighton, An Introductory Logic, chap. XI. 
Bode, An Outline of Logic, chap. vil. 
Joseph, An Introduction to Logic, chap. xvi. 
Welton, Manual of Logic, vol. I, bk. iv, chap. v. 



CHAPTER XIV 

FALLACIES IN ARGUMENTATION 

What a Fallacy is. A fallacy is, broadly speak- 
ing, an error in reasoning. This error may occur at 
any step. We may misinterpret our perceptions, or 
classify things wrongly, or work out bad definitions, or 
confuse ideas, or draw invalid conclusions from prem- 
ises. The risk of misjudgment is constantly present. 
The task confronting the human mind is twofold, that 
of attaining knowledge and that of handling it properly 
after it has been attained ; and neither part of this task is 
easy. Mistakes are constantly being made. But since 
human beings must think, because of the very require- 
ments of their life, the best they can do is to examine 
every stage and aspect of thinking in order to reduce 
mistakes to a minimum. It was this need which gave 
rise to logic. We may say, then, that thinking is an 
adventure and that fallacies are misadventures. 

A Classification of Fallacies. The traditional 
classification of fallacies is into 'deductive' and 'induc- 
tive ' fallacies. We shall interpret this classification as 
corresponding to the twofold task referred to above. 
Man must correctly handle the knowledge he already 
has, both in his private thinking and in his arguments 
with other people ; and he must be able to make inves- 
tigations into new fields. Where errors creep into one's 
own thinking or into argumentation, although no es- 
sentially new data or principles are involved, we have 



1 42 THE ESSENTIALS OF LOGIC 

to do with 'deductive' fallacies or fallacies in argu- 
mentation; where, on the other hand, errors arise in 
attempts to extend the boundaries of knowledge, they 
are better called 'inductive' fallacies. In the present 
chapter, we are concerned primarily with the former. 

Classification of Deductive Fallacies. It is dif- 
ficult to get a single positive principle of classification 
for fallacies. The usual division is into ' formal ' and 
4 material.' Formal fallacies are those which involve 
some breach of the logical rules of the syllogism. Since 
obversion and conversion are closely connected with the 
syllogism, false conversion and false obversion may be 
placed here. Material fallacies result from a misappre- 
hension of the content or from false assumption. 

Formal fallacies have been treated in detail in con- 
nection with the chapters devoted to the syllogism. I 
shall run over the list and suggest that the student 
seek to clear up his memory in regard to them. They 
are as follows : (1) False conversion ; (2) False ob- 
version ; (3) Four Terms; (4) Undistributed Mid- 
dle; (5) Illicit Major ; (6) Illicit Minor ; (7) Two 
Negative Premises ; (8) Two Particular Premises ; 

(9) Affirmative Conclusion with Negative Premise; 

(10) Denying the Antecedent; (11) Affirming the 
Consequent ; (12) Incomplete Disjunction. Of these, 
special stress should be put on the Undistributed Mid- 
dle and the fallacy of Four Terms. All verbal fallacies 
appear syllogistically as Four Terms. Whenever the 
middle term is vague or indefinite, there is danger of 
an ambiguous middle. While M is jP, yet S may bo 
M with a difference. 

Material fallacies fall into two main divisions, those 



FALLACIES IN ARGUMENTATION 143 

connected with definition and those involving unwar- 
ranted assumption. If terms are not clearly defined, 
some form of ambiguity is almost sure to appear. On 
the other hand, the logic of argumentation demands 
that the conclusion be not assumed but deduced from 
accepted premises. The following classification will 
serve as a guide : — 

Material Fallacies 

Fallacies of Equivocation Fallacies of Unwarranted 

Assumption 

1. Ambiguous and Shifting 1. Begging the Question. 
Terms. 2. Complex Question. 

2. Amphiboly. 3. Irrational Evidence. 

3. Composition. (a) Argumentum ad hominem. 

4. Division. (b) Argumentum ad populum. 

5. Accident. (c) Argumentum ad ignoran- 

6. Accent. tiam. 

7. Figure of Speech. (c?) Argumentum ad vericun- 

diam. 

4. Irrelevant Conclusion. 

5. Non sequitur. 

Fallacies of Equivocation. 1. Words may be in- 
definite and yet not ambiguous. When, however, there 
is the slightest danger of misunderstanding, words 
should be defined or else clearly qualified by the con- 
text. In literature, the suggestiveness of a word may 
depend upon its capacity to awaken many lines of asso- 
ciation. But precision rather than suggestiveness is fun- 
damental for reasoning. Especially is this the case in 
long arguments in which the meaning of a term may 
$hift from stage to stage if care be not taken. For in- 
stanee, an argument may start with legal right and 
conclude with moral right. The following fallacious 



144 THE ESSENTIALS OF LOGIC 

syllogism may serve as an example of a subtle form of 
equivocation called c Ambiguous Middle ' : — 

All able men are consistent with themselves; 

He who changes his opinions is not consistent with himself; 

He who changes his opinions is not an able man. 

A moment's reflection shows that the reference to 
time is different in the two premises. 

2. When the ambiguity lies in the very structure of 
the sentence, the resultant fallacy is called * Amphib- 
oly.' The sentence permits of a double interpretation. 
Such cases as occur to-day are accidental and have 
little significance except as a warning against careless 
writing. The following want-advertisements are good 
examples : — 

Wanted: a groom to look after two horses of a pious turn of 
mind. 1 

A second-hand morris-chair is wanted by a bachelor with richly 
carved claw-feet. 

The classical cases of Amphiboly are the decrees of 
the oracle at Delphi. The response of the oracle to 
Pyrrhus is an excellent instance: "Pyrrhus the Ro- 
mans can, I say, subdue." 

3. The fallacy of Composition arises when an attri- 
bute is predicated of a whole, which holds only of a 
part. The object to which the property is fallaciously 
assigned is usually an aggregate. Thus, to argue that 
a country is prosperous because many business men 
are making money, is essentially to commit the fallacy 
of Composition. Very similar to this is the following 
argument : — 

1 Gibson, The Problem of Logic. 



FALLACIES IN ARGUMENTATION 145 

The manufacturers of woolens are benefited by the duty on 
woolen goods; the manufacturers of cotton by the duty on cotton; 
the farmer by the duties on wool and grain; and so on for all the 
other producing classes; therefore, if all the products of the 
country were protected by an import duty, all the producing 
classes would be benefited thereby. 

It will be noted that the mind easily tends to pass 
from individual cases and classes to larger wholes with- 
out thought of the new influences and relations which 
are at work in such a whole. 

4. The fallacy of Division is the converse of Com- 
position. It consists in the assignment to the part of 
attributes which are true only of the whole. We can 
bring this fallacy into touch with the distinction be- 
tween the collective and the distributive use of terms 
by saying that it arises from a disregard of these two 
uses. In the major premise, the term may be used col- 
lectively, while it is employed distributively in the 
minor. The following example illustrates this hasty 
movement from the whole to the parts : — 

He cannot be innocent, for he was a member of the mob which 
committed the deed. 

We are especially liable to fall into this error in 
discussions upon social and political topics. Because 
people act rather foolishly or selfishly as units in a 
group, it does not follow that their conduct will be of 
the same character when they are acting as individuals. 
As one writer has forcefully put it, individual morality 
has outstripped crowd morality by many centuries. 
" Perhaps the commonest form of the fallacy is that 
which it takes in such arguments as, 4 It must be 
wrong for you to act in this manner, because if every 



146 THE ESSENTIALS OF LOGIC 

one did so, the consequences would be disastrous/ We 
start by urging that if A and B and C . . . (conjunc- 
tive) acted in some specified manner — the welfare of 
the world would be fatally affected, and we go on to 
argue that no less fatal consequences must follow 
when A or B or C (disjunctive) act in the manner 
specified." * 

5. The fallacy of Accident consists in the applica- 
tion of an abstract principle without allowance for 
qualifying conditions. Because water boils at 212° 
Fahrenheit and such water will boil an egg in five 
minutes, it does not follow that boiling water on the 
top of a mountain will cook an egg in that number of 
minutes. Because charity is a virtue, we must not con- 
clude that it is necessarily virtuous to give a beggar a 
dollar. It may do him more harm than good. Such ab- 
stract principles are not true universals and the mis- 
take lies in so taking them. In argument, it is so easy 
to make general pronouncements and shove to one side 
those qualifications which a keener desire for truth 
would take account of. u There is no fallacy more in- 
sidious than that of treating a statement which for 
many purposes is true as if it were true always and with- 
out qualification." 2 

The converse fallacy of Accident consists in the pas- 
sage from what is true under certain circumstances to 
an abstract principle based upon these instances. In- 
ductively, it takes the form of a hasty generalization. 
An individual who argued that a college education was 

1 Gibson, The Problem of Logic, p. 284. Cf. Welton, Manual of 
Logic, vol. ii, p. 247. 

2 Joseph, An Introduction to Logic, p. 549. 



FALLACIES IN ARGUMENTATION 147 

valueless because Edison and Ford did not have one 
would be committing this fallacy. The type of argu- 
ment is, I think, easily recognized. 

Both the direct and the converse fallacies of Acci- 
dent are important because they bear witness to a 
deep-seated tendency to think abstractly and dogmati- 
cally. Only the careful thinker does justice to both 
principles and facts. Lotze, a German philosopher of 
the last century, wrote the following very sane com- 
ment : " Two general modes of fallacious thought are 
developed by the habitual commission of these fallacies, 
and illustrate them on a grand scale. The first is doc- 
trinairism, the second narrow-mindedness. The doctri- 
naire is an idealist who refuses to see that though 
ideas may be right in the abstract, yet the nature of 
the circumstances under which and of the objects to 
which they are to be applied, must limit not only 
their practicality, but even their binding force. The 
narrow-minded, on the other hand, can recognize and 
esteem no truth and no ideal, even the most univer- 
sally valid, except in that special form to which they 
have become accustomed within a limited circle of 
thought and personal observation. Life is a school 
which corrects these habits of mind. The parochially 
minded man sees things persist, in spite of himself, in 
taking shapes which he considers unprecedented, but 
he finds the world somehow survives it, and learns at 
last that a system of life may be excellent and precious, 
but that it is rash from that to argue that it is the only 
proper mode of orderly existence. And the enthusiast 
for ideals, when he sees the curtailment which every at- 
tempt at realization inflicts on them, learns the lesson 



148 THE ESSENTIALS OF LOGIC 

which the disjunctive theorem might have taught 
him." 1 

6. The fallacy of Accent is due to a misleading 
emphasis. When words are taken from their context, 
they often seem to have a meaning which an investiga- 
tion shows was not the intent of the author. This error 
is near enough to misinterpretation caused by mis- 
placed emphasis to be classified with it. Another in- 
stance is the use of italics in a quotation where no 
words were originally italicized. Jevons points out a 
laughable case of the use of italics lending itself to 
misunderstanding. In the First Book of Kings, xiii, 27, 
the translators added a word to complete the sentence 
and put it in italics to indicate this fact. The result was 
as follows : " And he spake to his sons, saying, Saddle 
me an ass. And they saddled Aim." " It is curious," 
continues Jevons, " to observe how many and various 
may be the meanings attributable to the same sentence 
according as emphasis is thrown on one word or an- 
other. Thus the sentence, ' The study of logic is not 
supposed to communicate the knowledge of many use- 
ful facts,' may be made to imply that the study of 
logic does communicate such a knowledge, although it 
is not supposed to do so ; or that it communicates a 
knowledge of many useless facts." 2 

7. The fallacy of Figure of Speech is due to the 
ambiguous character of some verbal inflection. It is not 
of much importance in a language like English in which 
inflection is at a minimum. The best case, and the one 
usually quoted by logicians, is found in Mill's book, 
Utilitarianism. He is trying to prove that pleasure is 

1 Logic, vol. ii, p. 5 (Eng. trans.). 2 Lessons in Logic, p. 175. 



FALLACIES IN ARGUMENTATION 149 

the chief good. " The only proof," he writes, " capable 
of being given that an object is visible is that people 
actually see it. The only proof that a sound is audible is 
that people hear it : and so of the other sources of our 
experience. In like manner, I apprehend, the sole evi- 
dence it is possible to produce that anything is desirable, 
is that people actually desire it." But ' visible ' and ' au- 
dible ' mean what can be seen and heard, while ' desira- 
ble ' means what is worth desire or ought to be desired. 
Mill did not notice the change in meaning because he 
was paying too strict attention to the form of the words. 
A similar mistake is sometimes made when the original 
or etymological meaning of a word is stressed and the 
more usual meaning of the present disregarded. Thus, 
to argue that representatives must passively represent 
their constituents is to commit this fallacy. 

Fallacies of Unwarranted Assumption. These 
fallacies consist in the entrance into the argument of 
an unwarranted element of assumption. Either the 
point at issue is assumed (Begging the Question, and 
Complex Question), or the evidence adduced is irrele- 
vant (Irrational Evidence), or the conclusion is beside 
the point (Irrelevant Conclusion, and JVbn Sequitur). 
In all these cases, the conclusion is not demonstrated 
and the fallacy consists in the assumption that it is. 

1. Begging the Question, or Petitio Principii, is 
the assumption of the point to be proved. In an argu- 
ment, it consists in the taking for granted what an op- 
ponent would not admit if its significance were under- 
stood ; it is the " surreptitious assumption of a truth 
you are pretending to prove." 

There are two distinguishable types of question- 



150 THE ESSENTIALS OF LOGIC 

begging. In the one, the conclusion we wish to prove 
is directly assumed under another name ; in the other, 
some larger general principle which includes the point 
in dispute is taken for granted. 

The first type appears either as a question-begging 
epithet or as reasoning in a circle. To call a prisoner 
before the bar a worthless good-for-nothing whom every 
one has suspected for a long time is not to prove that 
he has committed the crime of which he is accused, but 
to prejudice the jury against him. Epithets are insidi- 
ous attempts to lead the minds of the listeners in the 
desired direction independently of genuine evidence. 
Nowhere is this procedure more frequently resorted to 
than in politics. Mud-slinging is the bane of political 
life, and, unfortunately, it has its bad ethical effect. 
Those who drop into the practice must lose some meas- 
ure of their intellectual integrity. Logic has its morali- 
ties. Reasoning in a circle consists in the use of a prem- 
ise which is only the desired conclusion stated in other 
words. It is difficult to offer a good example in brief 
compass of this species of Begging the Question, since 
it is more apt to occur in a long argument. Often argu- 
ments do not make any advance, but twist and turn and 
repeat the same things in different words. Absence of 
a clear-cut argument is nearly always a sign of an ele- 
ment of circular thinking. The individual tries desper- 
ately to make an advance, but really turns around the 
same fixed ideas with much noise of asseveration. It is 
a form of logical hemming and hawing. When there 
is a sophistic element, an intent to deceive and to se- 
cure victory at all hazards, reasoning in a circle becomes 
argument in a circle. A frequently used device in Eng- 



FALLACIES IN ARGUMENTATION 151 

lish is to state the proposition to be proved in words 
of Saxon origin and then to give as reason for it the 
same proposition in words of classical origin. The fol- 
lowing example from Whately is much quoted in this 
connection : " To allow every man an unbounded free- 
dom of speech must always be, on the whole, advanta- 
geous to the State, for it is highly conducive to the 
interests of the community that each individual should 
enjoy a liberty perfectly unlimited of expressing his 
sentiments." 

The second general type of question-begging consists, 
as we have said, in the assumption of a larger principle 
than the one in dispute from which this latter may be 
deduced. It has much in common with the fallacy of 
Accident. Thus, if a piece of legislation concerning a 
particular remediable wrong were under discussion, it 
would be question-begging to make appeal to some 
abstract principle, like ' All legislation which interferes 
with the right of free contract is bad.' At one time — 
in the past, I am thankful to say — certain abstract 
principles of political economy were used in this way 
as maxims against remedial legislation ; and we all know 
how both the conservative and the demagogue make 
use of slogans. 

In regard to this fallacy, it is well to bear in mind 
what De Morgan called its opponent fallacy : " It is 
the habit of many to treat an advanced proposition as 
a begging of the question the moment they see that, if 
established, it would establish the question." Such an 
attitude is not playing fair. 

2. When a question is so stated ^s to involve a ques- 
tionable assumption, it is called a ' Complex Question.' 



158 THE ESSENTIALS OF LOGIC 

Any direct answer to such a question implies the ad- 
mission of the point assumed. Complex Question may- 
be a trick as in the following examples : 4 Have you left 
off beating your wife?' 'Has the practice of heavy 
drinking ceased in your part of the country ? ' Or it 
may be due to the fact that the interrogator has not 
analyzed all that his question involves. A teacher in 
philosophy may be asked how he explains telepathy. 

3. " The characteristic appeal which Science, in its 
processes of reasoning, makes to the mind is the argu- 
mentum ad judicium, or appeal to reason. When the 
appeal is not to the impartial reason, but to the feelings, 
passions, prejudices of men, it is, from the logical point 
of view, radically irrelevant, and involves the fallacy of 
Irrational Evidence." 1 

This fallacy is akin to the first type of Begging the 
Question ; the difference lies in the openness of the ap- 
peal to the non-logical. Locke's treatment of the vari- 
ous forms of this fallacy is classic. " Of all the argu- 
ments," he writes, " that men ordinarily make use of, 
the argument ad judicium alone brings true instruction 
with it, and advances us in the way to knowledge. . . . 
For (1) it argues not another man's opinion to be right, 
because I, out of respect, or any other consideration but 
that of conviction, will not contradict him. (2) It proves 
not another man to be in the right way, nor that I ought 
to take the same with him, because I know not abetter. 
(3) Nor does it follow that another man is in the right 
way because he has shown me that I am in the wrong." 2 
Putting these conclusions into touch with the experience 

1 Gibson, The Problem of Logic, p. 287. 

2 Locke, Essay concerning Human Understanding, bk. iv, chap. xvn. 



FALLACIES IN ARGUMENTATION 153 

that any appeal to feeling must be regarded with sus- 
picion, logicians have distinguished the following varie- 
ties of Irrational Evidence : — 

(a) Argumentum ad hominem. In this fallacy the 
argument is directed against the character of the man 
who is the opponent instead of adhering to its proper 
task of proving the point at issue. Too often, calumny 
and gossip are resorted to in order to make out a case 
and win the decision. Here, again, logic touches upon 
ethics. If the ideal held is that the end justifies the 
means, such arguments come under rhetoric and the 
only point of attack is their effectiveness. They are 
more non-logical than illogical. As a matter of fact, 
they are usually employed by individuals who are fully 
aware of what they are doing. They are the tricks of 
the sophist. A story is told of O'Connell that on one 
occasion, when he had to defend a man who was clearly 
in the wrong, the counsel for the prosecution was a cer- 
tain Mr. Kiefe, who had come in for some money in 
rather a questionable way, and had taken the name of 
O'Kiefe. O'Connell commenced his defense by address- 
ing his opponent : — 

"Mr. Kiefe O'Kiefe, 
I see by your brief o'brief 
That you are a thief o'thief," — 

which so disconcerted Mr. O'Kiefe and so tickled the 
jury that a verdict was returned for the defendant. At 
least there was wit in this case of argumentum ad homi- 
nem. Any argument in which there is appeal to motives 
and facts which do not bear upon the objective truth 
of the position at issue can be classed under this title, 
(6) Argumentum ad populum is an appeal to the 



154 THE ESSENTIALS OF LOGIC 

feelings, passions, and prejudices of the group ad- 
dressed instead of to the intellect. Almost all political 
speeches and, I fear, nearly all writings which have 
become popular in times of excitement, have contained 
an ingredient of emotional incitement. The logician 
must follow the psychologist in the study of crowd 
psychology. He will then better know the power of 
suggestion. The individual thinks most clearly and in- 
dependently when he is alone. Let him be on his guard 
against suggestions of an emotional sort which do not 
leave a deposit of definable ideas. The thinker needs the 
will to analyze and the power to put passion and preju- 
dice far away from him. Let him remember that we call 
6 enthusiasm ' in ourselves and those who think like us 
what we call ' fanaticism ' in our opponents. The ideal 
of objectivity is not a bad thing to set before one. 

The best instance in literature of argumentum ad 
populum, according to one writer, 1 is Anthony's 
speech to the Roman mob in Shakespeare's Julius 
Ccesar. Let the student pick up his high-school copy 
and re-read the passage. 

A species of argumentum ad populum sometimes re- 
ferred to is argumentum ad misericordiam, an appeal 
to pity or sympathy for a cause or person when the 
facts do not warrant it. We Americans are soft-hearted 
and sometimes foolishly sentimental. 

(c) Argumentum ad ignorantiam consists in the 
attempt to throw the burden of disproof upon the other 
party to an argument. To maintain that telepathy is 
true just because it cannot be positively disproved is 
an example of such a policy. Mystics are constantly 

1 Taylor, Elementary Logic, p. 180. 



FALLACIES IN ARGUMENTATION 155 

resorting to this fallacy. As Creighton points out, the 
reasoning seems to be as follows : — 

It is not impossible that this is so; 
What is not impossible is possible; 
Therefore it is possible that this is so; 

Mere abstract possibility is not enough ; there must be 
some evidence of a factual character. 

(d) Argumentum ad vericundiam is an appeal to a 
man's modesty in the face of the reverence people feel 
for authority and tradition. It is fallacious because it 
involves the refusal to examine a case on its real merits 
and the willingness to give more weight to the ipse 
dixit of accepted authorities than to reason and fact. 
This fallacy is rooted in the conservative and conform- 
ist instincts of society. Locke felt the weight of the 
scholasticism of his day and his quaintly phrased pro- 
test is well worth quoting : " When men are established 
in any kind of dignity, it is thought a breach of mod- 
esty for others to derogate any way from it, and ques- 
tion the authority of men who are in possession of it. 
This is apt to be censured, as carrying with it too much 
pride, when a man does not readily yield to the deter- 
mination of approved authors, which is wont to be re- 
ceived with respect and submission by others." We 
must give weight to the views of men with established 
reputations, but there is no obligation to be too docile. 

Another form of the same fallacy is the tendency to 
transfer reputation from one field to another. To quote 
a famous inventor on a point of theology, an energetic 
business man on problems of broad statesmanship, or 
an explorer on questions of social ethics is to commit 
this fallacy. A man may be competent in one field and 



156 THE ESSENTIALS OF LOGIC 

have no special competence in another. The logician 
must try to hold before the mind the meaning and con- 
ditions of competence. To tell what constitutes proof 
is also to tell what is not proof. 

4. Irrelevant Conclusion consists in proving some- 
thing different from the actual point at issue. It is an 
evasion or ignoring of the proposition to be proved. 
" Instead of proving that • this prisoner has committed 
an atrocious fraud,' you prove that the fraud he is 
accused of is atrocious : instead of proving (as in the 
well-known tale of Cyrus and the two coats) that the 
taller boy had a right to force the other boy to exchange 
coats with him, you prove that the exchange would have 
been advantageous to both : instead of proving that the 
poor ought to be relieved in this way rather than in 
that, you prove that the poor ought to be relieved." x 

This fallacy is most easily committed in a long argu- 
ment in which the original question passes from the 
mind in the heat of the debate. One point leads to an- 
other, and, if some one of the contestants is not clear- 
headed, the concluding thesis is apt to be decidedly differ- 
ent from the beginning one. " The person who commits 
the fallacy of irrelevancy is, of course, quite unaware 
of his error, unless his purpose be to mislead. He does 
not see that the proposition which he proves is related 
to the point at issue only through a questionable assump- 
tion. But in criticizing an irrelevant argument it is not 
necessary to point out the nature of the assumption 
which underlies the argument. Merely to show that 
what is proved is not what ought to be proved or what 
is supposed to be proved, answers the purpose of criti- 

1 Whately, Elements of Logic, 



FALLACIES IN ARGUMENTATION 157 

cism. 4 True, but irrelevant,' is often the most concise 
and effectual criticism. 'Thus, when in a discussion 
one party vindicates, on the ground of general expedi- 
ency, a particular instance of resistance to government 
in a case of intolerable oppression, the opponent may 
gravely maintain that we ought not to do evil that good 
may come — a proposition which, of course, had never 
been denied, the point in dispute being whether resist- 
ance in this particular case were doing evil or not. Or 
again, by way of disproving the assertion of the right 
of private judgment in religion, one may hear a grave 
argument to prove that it is impossible every one can 
be right in his judgment.' The first of these arguments 
assumes, as a second premise, that ' this is a case of 
doing evil that good may come ' ; while the second takes 
for granted that 'if every one cannot be right in his 
judgment, then private judgment should not be per- 
mitted.' These assumptions, however, are highly ques- 
tionable, and until they are proved the arguments are 
beside the point." * 

All who have argued much with people are aware of 
how difficult it is to keep their attention fixed on the 
point which first arose for discussion. This tendency to 
wander off the track is the psychological cause of such 
irrelevancies as do not have a sophistic origin. 

5. Nan sequitur is the name usually now given to a 
conclusion which does not follow from the premises. 
The premises may be quite true, but they do not lead 
to the proposition which is attached beneath them. In 
the case of this fallacy, as in practically all of those 
which come under the caption, ' Unwarranted Assump- 
1 Bode, An Outline of Logic, pp. 103-04. 



158 THE ESSENTIALS OF LOGIC 

tion/ the argument in which it occurs is nearly always 
long-winded. If we are not very much interested in the 
assumption, or if we are not inclined to be analytic, a 
boldly advanced conclusion may be accepted at its face 
value. The following illustration of De Morgan's is a 
fair sample: — 

Episcopacy is of Scripture origin. 

The Church of England is the only Episcopal Church in Eng- 
land. 

Therefore, the church established is the church that should be 
supported. 

I am willing to hazard the opinion, that such an argu- 
ment, extended over many pages by means of historical 
details, would convince those who were already favor- 
ably inclined. 

Conclusion. The chief advantage in a summary dis- 
cussion of the fallacies lies in the training of the atten- 
tion it involves. It is a well-known principle of psy- 
chology that we can see best what we are looking for. 
Now, when we feel that an argument is fallacious, it is 
of great assistance to have in mind certain general 
types of fallacy which are possibly relevant. Once the 
classification is made, a standard interpretation and de- 
scription of the fault is within our grasp. 

REFERENCES 

Bode, A n Outline of Logic, chap. vni. 
Creighton, An Introductory Logic, chap. xn. 
Sidgwick, Fallacies. 
Whately, Elements of Logic, bk. ni. 



CHAPTER XV 

THE NATURE OF INDUCTION 

Induction and Deduction. Very often in the his- 
tory of a science, inappropriate terms fasten themselves 
on the terminology and are with difficulty removed. 
Logic presents us with such a case which is of the nature 
of a false contrast. Until very recently, it has been cus- 
tomary to divide logic into two distinct parts called, re- 
spectively, 'deductive' and 'inductive' logic. But it is 
being evermore clearly realized that this division is not 
satisfactory. What has been called ' inductive logic ' is 
really the logic of scientific method or the logic of all con- 
tinuous and systematic investigation in a comparatively 
new field where principles are still to be discovered. 
And the logic of systematic investigation deals with 
the whole of concrete reasoning ; it concerns itself with 
the discovery of facts, their classification, correlation, 
and explanation. 

If logic is the science of correct reasoning, it must 
examine the principles and methods used in such sys- 
tematic investigation. It must study the nature of syste- 
matic inference from facts and the construction of sys- 
tems of knowledge as well as the more formal principles 
of classification, definition, and syllogistic argumenta- 
tion. Logicians have realized this necessity and have 
given increasing attention to the larger field thus opened. 
As a consequence, every recent text devotes much of its 
space to scientific method and to the dangers which con- 
front the various stages of concrete inference. 



160 THE ESSENTIALS OF LOGIC 

Now, when we examine concrete reasoning which 
does not take its facts and principles for granted, we 
discover that it includes both induction and deduction. 
These are really supplementary and inseparable phases 
of any complete act of reasoning. The mind passes back 
and forth between fact and theory, evidence and infer- 
ence, and, in so doing, both elements are modified. In 
other words, principles and hypotheses are always ten- 
tative and experimental, while facts need selection and 
interpretation. 

The term ' induction ' is often used roughly for the 
passage from facts and less general propositions to laws 
and more general propositions ; while ' deduction ' refers 
to the process of analyzing ideas and using them in the 
interpretation of facts. As we proceed, we shall realize 
ever more clearly that the solution of any problem in- 
volves the continuance of this double movement in the 
course of which facts are gathered, selected, and inter- 
preted, and principles are suggested and developed. In- 
duction is, then, only a phase of concrete reasoning or 
investigation ; it is not a process which can exist apart. 
But because we have neglected this phase, relatively, up 
to now and have laid stress upon language, definition, 
and the syllogism, we must emphasize it in the follow- 
ing chapters. 

A Glance at the History of Logic. What we 
have wished to point out is that the terms, i deductive ' 
and 6 inductive,' were applied to the older and newer 
phases of logic as the result of an historical accident 
and that they are misnomers. The older logic tended 
to be static and to stress consistency and implication, 
while the newer developments were filled with the spirit 



THE NATURE OF INDUCTION 161 

of science and stressed its methods and mode of inves- 
tigation ; the older logic was one of consistency and 
order, the newer was one which concerned itself with 
the laws of systematic and progressive inference. Now, 
the syllogism, which shows how a conclusion follows in- 
evitably from the subsumption of an instance under a 
rule, was the dominant element in the older logic and 
this was therefore called 4 deductive ' ; the movement 
from fact to law was the conspicuous feature of the 
newer developments and the resultant logical doctrines 
were classified together as * inductive.' Thus these terms 
stood for an historical contrast. 

But this historical contrast has lost its sharpness with 
the lapse of time. There is no longer need to thunder 
against the scholastics as did Locke and Francis Bacon. 
Logic is, after all, one science and not two. The old 
factions have disappeared, and thinkers on logic see 
clearly that consistency and growth are not opposed to 
each other. The older logic has consented to be modi- 
fied by the spirit of the new. Logic has become less 
formal all along the line, and lays more stress upon the 
material of thought and the importance of purpose. 

Since we have not taken much space for the history 
of our subject, a brief reference to the purposes domi- 
nating logic at different epochs may be advisable. " Per- 
haps the simplest way of disentangling the leading 
features of the departments of Logic is to take them in 
relation to historical circumstances. These features are 
writ large, as it were, in history. If we recognize that 
all bodies of doctrine have their origin in practical 
needs, we may conceive different ages as controlled 
each by a distinctive spirit, which issues its mandate 



1G2 THE ESSENTIALS OF LOGIC 

to the men of the age, assigning to them their distinc- 
tive work. The mandate issued to the age of Plato and 
Aristotle was, Bring your beliefs into harmony one 
with another. The Aristotelian logic was framed in re- 
sponse to this order: its main aim was to devise instru- 
ments for making clear the coherence, the concatena- 
tion, the mutual implication of current beliefs. The 
mandate of the Mediaeval Spirit was, Bring your be- 
liefs into harmony with dogma. The mediaeval logic 
was contracted from Aristotle's under this impulse. 
Then, as science developed, a new spirit was roused the 
mandate of which was, Bring your beliefs into har- 
mony with facts. It was under this impulse that a body 
of methodical doctrine vaguely called Induction gradu- 
ally originated." * 

Now, the first and last mandates, at least, are perma- 
nent ones which will always correspond to a need of 
human life. Must we not always try to bring our beliefs 
into harmony with one another and with fact ? In exposi- 
tion there is a good pedagogical reason for treating the 
logic of consistency first ; it is such a systematic body 
of doctrine pivoting around the syllogism. But in the 
logician's thought it must be brought into touch with 
concrete reasoning in order to gain in vitality. The 
student, also, must be prepared to make this synthesis. 

The Function of the Syllogism. The chief aim of 
logic for many centuries was, then, to determine the 
conditions of correct conclusion from accepted premises. 
Because of this limited aim the syllogism was the pivot 
around which logical analysis turned. This simplifica- 
tion of logic had its advantages, but likewise its disad- 
1 Minto, Logic, Inductive and Deductive, pp. 243-44. 



THE NATURE OF INDUCTION 163 

vantages. Because the syllogism was not seen in its 
larger setting as only a part of actual reasoning, it was 
formalized and mechanized. The chief difficulties of 
creative thinking were ignored. While the keener 
minds were aware that it gave only a logic of consist- 
ency and order, the majority deluded themselves into 
assuming that it was an instrument of truth and of 
genuine inference. This misinterpretation was, how- 
ever, due largely to the time-spirit of dogmatism which 
prevailed for so long a period. With the advent of sci- 
ence, logic went into the melting-pot and is only gradu- 
ally re-forming in the mould of a wider outlook and a 
truer perspective. The syllogism still remains intact, 
but a juster view of its function is held. It is now seen 
that its function and even its character depend upon 
the purpose which is uppermost. 

When the purpose is the limited one of testing the 
consistency of a given argument, the syllogism is a 
valuable instrument. It offers a technique by which the 
argument can be analyzed and its parts seen in their 
mutual relations. We can decide whether all the ele- 
ments of a complete argument are present, whether the 
terms are really only three in number, whether the mid- 
dle term has the same meaning in the two premises, 
whether the conclusion follows, etc. In short, the syllo- 
gism and its theory presents the would-be analyst with 
satisfactory methods for his task. He knows what to 
demand and where the dangers lie. Relatively to this 
purpose, the syllogism can no more be outgrown than 
human thought itself. 

But this purpose is, after all, a narrow one. We are 
more frequently interested to-day in the increase of 



164 THE ESSENTIALS OF LOGIC 

knowledge and in its factual verification. We want to 
see how knowledge grows through investigation and the 
formation of hypotheses. We are more inclined to go 
back of the premises of an argument and to consider 
principles for which evidence is not advanced as dogmas. 
Moreover, probability plays a larger part to-day than 
ever before, and it will be remembered that the syllo- 
gism is suited only to certainty. Hence argument is 
not so easy a matter as it once was. Not only must an 
argument be self -consistent ; it must also be consistent 
with the facts. But purposes can coexist ; the narrower 
ideal of formal consistency has its validity just as has 
the wider purpose. The wider purpose must be able to 
include the narrower. 

When the syllogism is a part of inductive-deductive 
reasoning, the premises are essentally tentative : they 
lead to a certain conclusion ; but if this conclusion 
does not agree with the facts, the premises must be 
modified. The syllogism is a phase of a larger process. 
We shall understand this aspect of the case better 
when we come to consider the part played by hypothe- 
ses in modern science. It is important to us at present 
chiefly as showing how the older doctrines are being 
modified by a larger setting. 

Why the Syllogism is only a Fart of Reasoning. 
In the formal doctrine of the syllogism, the most diffi- 
cult problems of actual thinking are disregarded. If 
your opponent is kind enough to grant you certain 
premises, he is undoubtedly obliged to admit the truth 
of the implied conclusion. But whence do these prem- 
ises come? And is your opponent obliged to admit 
their truth? If he does not, the argument is at a 



THE NATURE OF INDUCTION 165 

standstill until premises are agreed upon. Otherwise, 
the syllogism involves a begging of the question. It is 
obvious that the syllogism is a part of a larger whole 
unless appeal to intuition is permitted. 

Let us verify this conclusion by an examination of 
the three kinds of syllogism. The categorical syllogism 
deals with classes, but it does not tell us how classes 
are formed and tested. Yet such formation and testing 
constitute one of the most difficult tasks of science. If 
we bear in mind the fact that real argument arises 
only as the result of doubt and perplexity, we can ap- 
preciate the importance of the processes largely pre- 
liminary to the syllogism. All syllogisms require at 
least one universal proposition, but universal proposi- 
tions do not grow on every bush. 

The hypothetical syllogism is in essentially the same 
situation. The major premise states a universal or nec- 
essary connection between an antecedent and a conse- 
quent. But such principles must first be achieved, and 
they represent the maturity of a science rather than 
its beginning. Otherwise, they are essentially experi- 
mental. So long as the major is tentative, the conclu- 
sion is a challenge to fact ; but then the syllogism be- 
comes a part of a progressive movement of knowledge. 

The disjunctive syllogism is obviously in the same 
situation. The alternatives must be complete and mutu- 
ally exclusive. But the attainment of such alternatives 
in any new field is not an easy matter. Of course, it 
is an easy matter to work up such alternatives as 
honest and dishonest, truthful and untruthful. These 
are simple contradictories and are not apt to lead to 
confusion. But to prove that certain theories alone 



166 THE ESSENTIALS OF LOGIC 

hold the field is an achievement lying back of the 
disjunctive syllogism. 

Steps in Systematic Investigation. There are 
at least four stages in any systematic investigation. 
These have been stated variously, and certain writers 
have felt themselves compelled to break up one or 
more of the stages into parts. I must warn the student 
against supposing that these stages are temporally dis- 
tinct so that one stage can be completed before the 
next begins. The mind of the true investigator keeps 
them as contemporaneous as possible, and passes up 
and down his chain of reasoning from fact to theory 
and from theory to fact. In a sense, the active thinker 
observes while he theorizes and theorizes while he 
observes. 

The first stage in systematic investigation is obser- 
vation ; the second is the formation of hypotheses ; the 
third is the development of these hypotheses ; and the 
fourth is their progressive testing and verification by 
renewed observation. These steps are fairly separable 
for logical analysis though they do not exist in such 
isolation in actual investigation. Each stage is con- 
fronted by characteristic dangers and involves logical 
and psychological principles of importance. Only by 
means of this massive and systematic advance with its 
constant hazards is new knowledge obtained. 

Three Elements in Investigation. There are 
three elements or distinguishable mental processes in all 
investigation. We may call the first the inductive ele- 
ment par excellence. In both observation, the begin- 
ning of investigation, and verification, its end, the 
stress is laid upon facts. The essential principle of 



THE NATURE OF INDUCTION 167 

this element in the attainment of knowledge is fidelity 
to relevant fact. Science has always stressed fact as 
the beginning and only firm foundation of knowledge. 

The second element is the formation of hypotheses. 
The creative investigator must be capable of making 
fruitful conjectures as to the relations which hold be- 
tween facts or lie back of them. He must have what 
one psychologist speaks of as a creative imagination. 
Francis Darwin in his biography of his father remarks 
as follows : " He often said that no one could be a 
good observer unless he was an active theorizer. This 
brings me back to what I said about his instinct for 
arresting exceptions ; it was as though he were charged 
with theorizing power ready to flow into any channel 
on the slightest disturbance, so that no fact, however 
small, could avoid releasing a stream of theory, and 
thus the fact became magnified into importance." We 
shall have much to say of this constructive, conjectural 
element as we proceed. 

The third element is the deductive reasoning out of 
the implications of hypotheses and theories to see what 
they imply in the light of knowledge already possessed. 
Some writers in logic speak of this element as < de- 
ductive inference ' ; others speak of it as ' reasoning.' 
In any case, the significance of the hypothesis is devel- 
oped as completely as possible and its implications 
noted. These implications lead back to the sphere of 
fact again and so we return to the inductive element. 

The Problem of Generalization. As has been well 
said, syllogism never generalizes. How, then, do we 
secure universal or semi-universal propositions to serve 
as premises ? The difficulty arises from the fact that 



168 THE ESSENTIALS OF LOGIC 

experience gives us only particular events and things. 
We note that this medicine seems to have a beneficial 
effect, and that this piece of metal has certain proper- 
ties ; but how do we go beyond the instance to a rule ? 
We must, first of all, be careful to set the problem 
correctly. Modern psychology informs us that every 
instance is interpreted in the light of past experience 
at the time it enters consciousness. Things and events 
are noted as members of a familiar class or as members 
of a potential class. Observation and generalization, 
perception and interpretation, sensation and association 
go hand in hand. We interpret as we perceive and gen^ 
eralize as we observe. The mind is, moreover, selective 
and stresses what is regarded as important or even essen- 
tial. If this medicine cures an ill, then curing this kind 
of ill is an essential property of this kind of medicine. 
We expect classes and other instances. Why ? Because 
it is the very nature of the mind to note similarities 
and differences and so to classify. " It is for the sake 
of generalization that we observe at all, and the very 
act of observing intelligently is nothing else than the 
act of generalizing from what we observe." We do not 
so much pass from particular instance to particular in- 
stance as from a beginning class to a growing class. 

A little reflection must convince us that the mental 
process leading to generalization does not depend upon 
the application of any consciously held principle — even 
though its logical validity may imply some such princi- 
ple. As writers since the days of David Hume have 
pointed out, the child unconsciously generalizes things 
and events and builds up practical rules to act upon. 
Wild plums are very sweet when they are ripe ; fish 



THE NATURE OF INDUCTION 169 

bite best on cloudy days ; the river will be swollen after 
a rain ; a circus always has a band, etc. Such classifica- 
tions are gradually built up because the process of gen- 
eralization continually repeats itself in our minds ; and 
our lives are guided at every moment by the maxims 
and rules thus obtained. What science does is to ex- 
tend experience and to control it by completer analysis 
and experiment. It does reflectively and methodically 
what common sense has been doing all along. 

This tendency to put two and two together, to regard 
one thing as an indication of another, is evidently a part 
of our mental constitution. This linkage of terms com- 
bined with the recognition of likenesses and differences 
accounts for a large share of what we call reasoning. 
Professor Dewey goes so far as to assert that the estab- 
lishment of one thing as a sign of another is the cen- 
tral factor of thinking. " Reflection thus implies that 
something is believed in (or disbelieved in), not on its 
own direct account, but through something else which 
stands as witness, evidence, proof, voucher, warrant ; 
that is, as ground of belief At one time, rain is actu- 
ally felt or directly experienced ; at another time, we 
infer that it has rained from the looks of the grass and 
trees, or that it is going to rain because of the condi- 
tion of the air or the state of the barometer. At one 
time, we see a man (or suppose we do) without any 
intermediary fact ; at another time, we are not quite sure 
what we see, and hunt for accompanying facts that will 
serve as signs, indications, tokens of what is to be be- 
lieved." 1 

The Implication of Generalization. Logic does 

1 Dewey, How We Think, p. 8. 



170 THE ESSENTIALS OF LOGIC 

not impugn the act of generalization, but tries to under- 
stand what takes place and what principle is implied. 
It is evident that an event acquires meaning as a sign 
of another event so that an internal relation between 
them is developed in the mind. It is also apparent that 
any one event is regarded as typical of a class. We 
pass quickly from this event to an event of this class 
as soon as our minds are preparing to generalize. Sup- 
pose a savage goes out on a hunt for game, and, as he 
steps into the forest, a rabbit crosses his path. It hap- 
pens that he has no luck that day. If he is supersti- 
tious, he is liable to connect this lack of success with the 
appearance of the rabbit. But he has no reason to sup- 
pose that there is anything peculiar about this particular 
rabbit ; hence it sinks back into the class. It is the rab- 
bit as a recognizable class of animals that presages bad 
luck. Unless there is strong reason to the contrary, the 
individual instance tends to be merged in the idea of 
the class. Psychologically, the class is as primitive as 
the individual. 

But if the logician does not impugn the tendency to 
generalize, he is aware, nevertheless, that a principle is 
involved which must be valid if the generalization is 
valid. This principle or postulate is usually called the 
« Principle of the Uniformity of Nature.' We assume, 
consciously or unconsciously, that there are universal 
connections or relations in nature. This assumption, 
when formulated explicitly, is suggested by the way the 
mind works and the degree to which nature seems to 
recognize the tendency to relate terms as invariable 
signs of one another. But logicians have come to the 
conclusion that the principle cannot be proved by expe- 



THE NATURE OF INDUCTION 171 

rience, but can only be relatively confirmed by it. For 
this reason, it is frequently called a ' postulate.' 

How Generalization differs from Expectation. 
Animals develop expectations in much the same way 
that human beings do. A doctor's horse expects to turn 
in at a certain farmhouse because it has done so on 
previous trips. A dog anticipates a walk when his mas- 
ter takes down his hat from the wall. The formation 
of associations of this character is natural to the mind 
at fairly low levels as well as at the human level. Is 
generalization more than this ? Though based on it in 
part, it certainly goes beyond mere expectation. Other 
mental processes than those of association enter in. The 
animal glides from the one event to the other without 
holding them both before the mind as distinct objects of 
attention. But man does hold both terms of the rela- 
tion before his mind at one and the same time, and 
makes them and their internal connection a single com- 
plex object of thought. This the animal cannot do. We 
may say, then, that generalization is a higher develop- 
ment than expectation and depends upon the capacity 
to conceive two events as classes and to relate them in- 
ternally as somehow bound together. A generalization 
is a more or less explicit assertion that two terms are 
related. 

The Importance of Generalization. It may not 
be amiss to call attention once more to the importance 
of generalization. Were we literally confined to par- 
ticulars, we should be unable to reason. The very na- 
ture of reasoning is the passage from what is given to 
what is not directly given. As we say, we infer that 
so-and-so will happen because something else has oc- 



172 THE ESSENTIALS OF LOGIC 

curred. This something else is taken as a sign of the 
event inferred. Thus we apply rules to our present ex- 
perience in order to interpret it and to pass in concep- 
tion beyond it. But such rules can come only from 
generalization. 

Testing Generalizations. While we cannot prove 
the Principle of the Uniformity of Nature, we can test 
specific inductive inferences to see whether they really 
come under the principle. If they stand all the empiri- 
cal tests we can apply, we call them laws of nature. 
Science has for centuries been engaged in the discovery 
of laws of this character, laws which the hasty observa- 
tions and inadequate methods of common sense cannot 
discover. The generalizations of common sense are rules 
and maxims which hold in the main rather than laws 
which are universal or do not admit of exceptions. Why 
common sense is not able to formulate many universal 
propositions will become clearer to us as we proceed. 
Its maxims are not founded on analytic methods which 
exclude the irrelevant. The strength of science rests 
on the development of such methods and the technique 
which accompanies them. It is to the consideration of 
this technique and these methods in their general as- 
pects that we now turn our attention. 



REFERENCES 

Bode, An Outline of Logic, chap. ix. 

Creighton, An Introductory Logic, chap. xm. 

Dewey, How We Think, chaps. I and vn. 

Minto, Logic, Inductive and Deductive,bk. II, Introduction. 

Sidgwick, The Process of Argument, chaps, iv and vin. 



CHAPTER XVI 

THE GENERAL METHODS OF SCIENCE 

How Science developed. Science grew to its pres- 
ent stature by the efforts of men who attempted to 
solve problems which attracted their attention. There 
was much groping before suitable methods and a fairly 
satisfactory technique were worked out. The simplest 
aspects of nature were attacked before it was even pos- 
sible to approach the more complex fields. The growth 
of science was the result of the painstaking care and 
genius of such men as Galileo, Kepler, Newton, Lavoi- 
sier, Liebig, and others too numerous to mention. 
Their sagacity, fertility of suggestion, experimental in- 
genuity, and thoroughness led to the gradual accumu- 
lation of facts and the appearance of just notions about 
the constitution and mode of working of the inorganic 
realm. Bit by bit, problems were properly defined, in- 
vestigated, theorized over, experimented upon and ex- 
plained. The technique of measurement was evolved, 
mathematics applied, and instruments invented. Thus, 
step by step, facts were discovered and fundamental 
principles like the c laws of Kepler * and the theory of 
gravitation of Newton were enunciated. All this was 
a growth of the most subtle kind which substituted a 
world of laws and conceptual elements for the familiar 
mass of changing things. The early scientists were 
confronted by a world of happenings and of unana- 
lyzed things, and it was with the greatest difficulty 



174 THE ESSENTIALS OF LOGIC 

that they learned how to handle it and make it tell its 
secrets. Let the student try to remove from his thought 
of the world such ideas as mass, inertia, gravitation, the 
laws of motion, the chemical elements, energy, etc., and 
he will better understand how much he owes to the 
constructive genius of these men. 

Since our purpose is to understand, and do justice 
to, all the factors in systematic inference, we must not 
neglect the ways in which these typical fathers of sci- 
ence made their contributions. Probably there is no 
better example for study than Galileo. "In 1581, 
while watching a lamp set swinging in the cathedral of 
Pisa, he observed that, whatever the range of its oscil- 
lations, they were invariably executed in equal times. 
The experimental verification of this fact led him to 
the important discovery of the isochronism of the pen- 
dulum." Here we note the alert attention ready to 
notice and meditate upon features of the surrounding 
world which would escape the vast majority, and the 
experimental facility which enables the analyst to sep- 
arate out special factors and control their occurrence. 
During two years which he spent as a lecturer on math- 
ematics at the University of Pisa, " he carried on that 
remarkable series of experiments by which he estab- 
lished the first principles of dynamics and earned the 
undying hostility of bigoted Aristotelians. From the 
leaning tower of Pisa he afforded to all the professors 
and students ocular demonstration of the falsehood of 
the Peripatetic doctrine that heavy bodies fall with 
velocities proportional to their weights." l Galileo was 
a keen observer, a suggestive interpreter, and a clever 

1 Encyclopcedia Britannica, art. " Galileo." 



THE GENERAL METHODS OF SCIENCE 175 

inventor. He saw problems and had the ingenuity to 
meet them. 

The Need of Analysis. The progress of science evi- 
dently depends upon all the processes by means of 
which facts are gathered, analyzed, and interpreted. 
Such collection of data involves selection, and this se- 
lection is facilitated by processes of comparison and 
analysis. The purpose is to eliminate the irrelevant and 
accidental and to center attention on the important 
and essential. Whatever aids in this task is of primary 
importance for systematic inference. Only after surface 
appearances are passed and irrelevant but confusing 
circumstances eliminated can the problem be defined 
and its probable answer suggested. Analysis by com- 
parison and experimentation is the pre-condition of 
explanatory conceptions. 

But we must never forget that the determination of 
what is important and relevant is no easy matter and 
is, indeed, the outgrowth of that prior knowledge for 
which the scientist has served an apprenticeship. Every 
problem requires a more or less special method and 
technique, and these reflect the ideas which are in the 
mind of the investigator. If he have the wrong notion, 
he may lose much time and labor to no account until 
some fact, or facts, makes him realize that he has been 
guided by a false conception. Logic can give no royal 
road to discovery. It can only abet the teacher of sci- 
ence in making the student conscious of the best meth- 
ods, mental habits and ideals and warning him against 
the dangers of haste and dogmatism. 

The Value of Technique and Instruments. The 
scientific man is on his guard against hasty conclusions. 



176 THE ESSENTIALS OF LOGIC 

He knows how easy it is to be led into errors of fact 
or theory by his interests and prejudices. It is this 
awareness of the difficulties confronting valid induction 
that leads him to collect so many facts and to use in- 
struments wherever possible. " The technique of scien- 
tific inquiry thus consists in the various processes that 
tend to exclude over-hasty ' reading in ' of meanings ; 
devices that aim to give a purely ' objective ' unbiased 
rendering of the data to be interpreted. Flushed cheeks 
usually mean heightened temperature ; paleness means 
lowered temperature. The clinical thermometer records 
automatically the actual temperature and hence checks 
up the habitual associations that might lead to error in 
a given case. All the instrumentalities of observation 
— the various meters and -graphs and -scopes — fill a 
part of their scientific role in helping to eliminate 
meanings supplied because of habit, prejudice, the 
strong momentary preoccupation of excitement and an- 
ticipation, and by the vogue of existing theories. Pho- 
tographs, phonographs, kymographs, actinographs, seis- 
mographs, phethysmographs, and the like, moreover, 
give records that are permanent, so that they can be 
employed by different persons and by the same person 
in different states of mind, i.e., under the influence of 
varying expectations and dominant beliefs." 1 

The attention of the scientist is more sustained and 
his observations are more systematic and unprejudiced 
than those of the untrained man. He possesses a men- 
tal technique of habits as well as the technique of instru- 
ments. But with modern methods of education, no one 
should be without some tincture of these methods and 
1 Dewey, How We Think, pp. 87-88. 



THE GENERAL METHODS OF SCIENCE 177 

attitudes. Logic seeks to inculcate those mental quali- 
ties which make for good thinking, such as caution, care- 
fulness, thoroughness, orderliness, exactness, eritical- 
ness. In this sense, education is primarily the formation 
of logical dispositions, of " careful, alert, and thorough 
habits of thinking." 

The Importance of Measurement. Definite knowl- 
edge has developed step by step with the power to meas- 
ure phenomena. In the physical sciences at least, laws 
are equations between the measurable elements of phe- 
nomena. Hence the invention of new and more exact in- 
struments of measurement has usually led to marked 
advances in the analysis of nature. " It would be a mat- 
ter of great interest to trace out the dependence of this 
vast progress upon the introduction of new instruments. 
The astrolabe of Ptolemy, the telescope of Galileo, the 
pendulum of Galileo and Huygens, the micrometer of 
Horrocks, and the telescopic sights and micrometer of 
Gascoyne and Picard, Roemer's transit instrument, 
Newton's and Hadley's quadrant, Dollond's achromatic 
lenses, Harrison's chronometer and Ramsden's dividing 
engine — such were some of the principal additions to 
astronomical apparatus. The result is, that we now take 
note of quantities, 300,000 or 400,000 times as small as 
in the time of the Chaldeans." * 

Experimentation. The devising of experiments is 
one of the important elements in a scientific investiga- 
tion. An experiment works towards an analysis of nature 
and a control of the field under study which will make 
the important facts stand out clearly. The modern stu- 
dent desires to control the order of occurrence of his 
1 Jevons, The Principles of Science , vol. i, p. 315. 



178 THE ESSENTIALS OF LOGIC 

phenomena and to vary the factors which are present. 
Under such conditions, he is able to eliminate features 
and notice the effect, and to introduce new features and 
see what happens. Within certain limits, he can do 
with nature as he wishes and make it answer his ques- 
tions. Thus experimentation is a method of controlled 
analysis, synthesis, and variation which enables man to 
make combinations that could never be observed free in 
nature. 

There are essentially three advantages in experiment. 
We can vary the combinations and circumstances of 
things at will; we can produce factors at will which we 
might have to wait years for otherwise or even never 
obtain ; lastly we can overcome the rigidity of things as 
they ordinarily present themselves. The following ac- 
count of experimentation brings out very well its place 
in investigation : " All inductive methods rest upon the 
regulation of the conditions of observation and memory ; 
experiment is simply the most adequate regulation pos- 
sible of these conditions. We try to make the observa- 
tion such that every factor entering into it, together 
with the mode and the amount of its operation, may be 
open to recognition. Such making of observations con- 
stitutes experiment." 1 Ingenuity in experimentation is 
certainly one of the prime qualifications of an investi- 
gator in the physical sciences. Such men as Faraday, 
Liebig, Pasteur, Darwin, and Davy were noted for 
their fertility in ideas and methods. 

The first stage of a science is dominantly observational 
in its mode of gathering and testing facts. Many sciences, 
like geology, find it difficult to pass beyond this stage 

1 Dewey, How We Think, p. 91. 



THE GENERAL METHODS OP SCIENCE 179 

because of the nature of the material with which they 
have to deal. But the ideal, at least, in all the sciences 
is the testing of hypotheses by carefully planned ob- 
servations. We are all so familiar with the use of ex- 
periment in physics and chemistry that we scarcely give 
it enough thought, but the application of experimental 
methods to biology arid psychology is newer and not so 
familiar. Yet, in these fields, also, nature is being com- 
pelled to react to conditions which would be unlikely to 
occur apart from human purpose. It is evident, then, 
that experimentation is a method of investigation and 
that it is the servant of ideas which are seeking to find 
themselves verified. 

The Use of Experiment in Biology. Experimental 
biology dates back only a few decades and is only now 
being developed to the extent it deserves. It has been 
found that growing organisms can be interfered with at 
various stages in a grossly mechanical way without pre- 
venting the production of normal forms. " A particu- 
larly striking case is that of Clavellina, an ascidian, 
that is to say, an animal organism of considerable com- 
plexity. 4 You first isolate the branchial apparatus from 
the other part of the body (which other part contains 
heart, stomach, and most of the intestine), and then 
you cut in two in whatever direction you please. Pro- 
vided they survive and do not die, as indeed many of 
them do, the pieces obtained by this operation will each 
lose its organization (becoming a mere sphere of cells 
devoid of specialized structure) • • . and then will each 
acquire another one, and this new organization is also 
that of a complete little Clavellina. ' " * 

1 McDougall, Body and Mind, p. 240. 



180 THE ESSENTIALS OF LOGIC 

Experimentation in Psychology. James's pic- 
turesque description of the rise of experiment in psy- 
chology is well worth quoting in this connection : 
" Within a few years what one may call a microscopic 
psychology has arisen in Germany, carried on by exper- 
imental methods, asking of course every moment for 
introspective data, but eliminating their uncertainty by 
operating on a large scale and taking statistical means. 
This method taxes patience to the utmost, and could 
hardly have arisen in a country whose natives could be 
bored. Such Germans as Weber, Fechner, Vierordt, 
and Wundt obviously cannot ; and their success has 
brought into the field an array of younger experimental 
psychologists, bent on studying the elements of the 
mental life, dissecting them out from the gross results 
in which they are embedded, and as far as possible re- 
ducing them to quantitative scales. The simple and 
open method of attack having done what it can, the 
method of patience, starving out, and harassing to death 
is tried. . . . There is little of the grand style about 
these new prism, pendulum, and chronograph-philoso- 
phers. They mean business, not chivalry." 1 The an- 
alytic character of experimentation comes out clearly in 
this quotation. The experimenter tries to dissect and 
abstract, and he is helped in his effort by instruments 
and methods of control. 

The Statistical Method. In complex fields science 
has gradually been forced to methods of tabulation in 
which results are set down in their appropriate places 
and averaged. The observation of specific things has 
given way to the gathering and arrangement of data. 

1 Principles of Psychology , vol. I, p. 192. 



THE GENERAL METHODS OF SCIENCE 181 

Only after these data are collected and tabulated is 
there any attempt made to interpret them and to draw 
the proper inferences. Combined with statistical meth- 
ods is the use of averages of various sorts, such as the 
arithmetical, the ' weighted,' the geometrical, the mode, 
and the median. 

Statistical methods are particularly employed in 
fields where experimental analysis cannot be obtained. 
Thus there is much use of statistics in the social sci- 
ences and in such a field as meteorology. After the 
4 primary statistical quantities ' are gathered, they must 
be arranged in tables in such a manner as to bring out 
important correlations. As we shall see when we take 
up the method in more detail, there are many possibili- 
ties of fallacy in both the gathering and the manipula- 
tion of statistics. 

The Method of Graphs. When relations between 
variables are complex and cannot be easily intuited, 
resort is increasingly had to the use of graphs. In a 
graph, a curve is plotted to bring out in a spatial way 
the relation involved. In this way, the correlation be- 
comes visible to the eye and is grasped without dif- 
ficulty. The interesting thing is, that such projection 
of variable quantities often leads to the discovery of re- 
lations which the investigator would not otherwise have 
noticed. 

Graphs are used in statistical investigation as a means 
of bringing out the import of the data in a vivid way. 
We are all familiar with this use of diagrams to illus- 
trate the comparative populations of the various coun- 
tries, or the relative sizes of their armies and navies, or 
the wheat production in different years. Investigations 



182 THE ESSENTIALS OF LOGIC 

in criminology are usually condensed by the aid of 
graphs. In brief, the graphical method is one both of 
investigation and of exposition. 

The Function of Hypotheses. In our treatment 
of scientific method, we have thus far called attention 
to the more external processes and technique which sci- 
ence has developed. But we must never forget that these 
processes require an informing spirit to guide them. 
There must always be a purpose at work and some 
fairly specific problem in sight before this machinery 
begins to move. To become familiar with the technique 
and instrumentation of science does not make a creative 
scientist ; nor is it enough to stare passively at test- 
tubes and microscopes. Facts are not objects to be col- 
lected like pebbles. They are not things which stand 
out in the environment with an external unity and 
identity of their own, but are dependent for their exist- 
ence, in one sense, and certainly for their perception, 
upon the mind of the investigator. Facts do not pass 
into the mind ready-made, nor do they offer themselves. 
The scientist must be on the watch for them and must 
aid them to express themselves. His mind must be 
sensitive to them. Without mental activity, it would be 
impossible to gather facts. Why is this ? It is founded 
on the very nature of voluntary attention. We attend 
to what we are interested in ; other things pass unr 
noticed. 

The facts connected with any investigation must be 
relevant facts. And this word gives us our clue. To be 
relevant is to be related to a purpose and a set of ideas. 
We must have some standard of selection, some way of 
telling what is important and what is unimportant. 



THE GENERAL METHODS OF SCIENCE 183 

There is a hazard in this, but the investigator must 
always take his chance. The warning that science gives 
by its history is general, and the individual scientist 
must make his own judgments and collect his own in- 
stances. 

While the mind must be active in observation, it 
must be still more active, and certainly more creative, 
in experimentation. Some theory or hypothesis is always 
at the basis of an experiment. The experimenter has 
some idea of what he expects to find. The experiment 
is, in fact, usually devised consciously to test a concep- 
tion which has gained favor. If oxygen is the essential 
factor in combustion, then its removal should prevent it. 
The resultant experiment is the crucial instance for the 
theory. If we are forced to deny a consequent, we are 
forced to deny the antecedent likewise, and to reject 
the idea which was gaining ground. It was in such a 
way as this that the phlogiston theory, which held sway 
before oxygen was discovered, was disposed of. 

In a later chapter we shall have more to say of the 
origin and function of hypotheses. What we wish to 
stress just now is the activity of the mind in every 
stage of investigation. To leave out the mind is like 
removing Hamlet from the play. 

REFERENCES 

Dewey, How We Think, chap. vn. 

James, Principles of Psychology, vol. I, p. 192/. 

Jevons, Principles of Science, vol. I, chap. xv. 

Merz, History of European Thought, vols. I and II, passim. 

Welton, Manual of Logic, vol. II, chap. VI. 



CHAPTER XVII 

OBSERVATION AND FACT 

The Need of Observation. Since the principle 
which should control all investigation is fidelity to rele- 
vant fact, we must emphasize the part played by obser- 
vation. Mere speculation uncontrolled by fact is almost 
certain to lose touch with reality. It may lead to the 
construction of beautiful systems but these systems for 
all their splendor and subtlety are sure to lack value 
as means of interpreting the world in which we actu- 
ally live. True systems of knowledge must be given a 
factual foundation. Fact is both the stimulus to, and 
the test of, knowledge. But fact can be obtained only 
by observation, direct or indirect. The investigator 
must either gather his data himself or else trust to the 
testimony of others. The precept which the logician 
feels called upon to enforce is that the observational 
side of investigations should be thorough and unbiased. 
Only in this way can data approach that objectivity 
which is the ideal of logical thought. 

The Difficulty of securing Data. The sources of 
knowledge, so far as facts are concerned, are direct and 
indirect. The only direct way is by means of personal 
observation, and this involves perception. Even mem- 
ory must be regarded as an indirect source since mem- 
ory is the more or less correct revival of what has once 
been experienced. Another motive for classifying mem- 
ory among the indirect sources of knowledge is the 



OBSERVATION AND FACT 185 

greater danger of mistake. Slight, if not gross, errors 
in memory are so frequent that careful thinkers feel 
compelled to take the greatest precautions and to insti- 
tute some method of record which will serve as a sub- 
stitute for the details which are so easily forgotten or 
changed. 

Conditions of Accurate Observation. The psy- 
chologist informs us that we notice only the things 
which interest us. Many stimuli come to our senses 
which never pass into consciousness because they do 
not awaken even a passing attention. This control of 
observation by interest is strikingly exemplified by the 
different accounts of events given by eye-witnesses. 
The records of the law courts are full of such conflict- 
ing testimonies on the part of eye-witnesses, and the 
experimental psychologist has been making experi- 
ments to study the degree of accuracy to be expected. 
The following example may make clearer the difficulty 
in securing trustworthy data when the series of events 
to be observed is complex : " A few years ago a painful 
scene occurred in Berlin, in the University Seminary 
of Professor von Liszt, the famous criminologist. The 
Professor had spoken about a book. One of the older 
students suddenly shouts, 'I wanted to throw light 
on the matter from the standpoint of Christian mor- 
ality ! ' Another student throws in, ' I cannot stand 
that ! ' The first starts up, exclaiming, ' You have in- 
sulted me ! ' The second clenches his fist and cries, ' If 
you say another word — ' The first draws a revolver, 
The second rushes madly upon him. The Professor 
steps between them and, as he grasps the man's arm, 
the revolver goes off. General uproar. In that moment 



186 THE ESSENTIALS OF LOGIC 

Professor Liszt secures order and asks a part of the 
students to write an exact account of all that has hap- 
pened. The whole had been a comedy, carefully planned 
and rehearsed by the three actors for the purpose of 
studying the exactitude of observation and recollection. 
Those who did not write the report at once were, part 
of them, asked to write it the next day or a week later ; 
and others had to depose their observations under cross- 
examination. The whole objective performance was cut 
up into fourteen little parts which referred partly to 
actions, partly to words. As mistakes there were counted 
the omissions, the wrong additions, and the alterations. 
The smallest number of mistakes gave twenty-six per 
cent of erroneous statements ; the largest was eighty per 
cent. The reports with reference to the second half of 
the performance, which was more strongly emotional, 
gave an average of fifteen per cent more mistakes than 
those of the first half. Words were put into the mouths 
of men who had been silent spectators during the whole 
short episode ; actions were attributed to the chief par- 
ticipants of which not the slightest trace existed ; and 
essential parts of the tragi-comedy were completely 
eliminated from the memory of a number of witnesses." l 
In such cases there is hardly such a thing as pure per- 
ception. Suggestion, imagination, and inference shoot 
through what is called i perception.' It is obvious 
that it is not very easy to find fact even when we wish 
to be faithful to it. But forewarned is at least fore- 
armed. 

In physical science the facts to observe are seldom 
as complex as in social matters. Yet the warning is not 

1 Miinsterberg, On the Witness Stand, pp. 49-50. 



OBSERVATION AND FACT 187 

out of place in the physical field. The chief advantage 
which the scientist has is that he can repeat his facts 
until he is satisfied that he has them correctly. 

Haphazard observation occurs when there is no very 
definite purpose back of the series of perceptions. 
Things and events are then noted at random according 
to the interests and associations which happen to come 
uppermost. When such haphazard observations are ex- 
amined, they are nearly always found to be too inac- 
curate or fragmentary to be of much value. We see, 
then, that one of the prime conditions of good obser- 
vation is definiteness of purpose. The investigator must 
be on the outlook for facts of a known character or he 
will miss them. We are all aware that we are more apt 
to find a lost article if we know what to look for. The 
scientist who is carrying on an investigation has a 
fairly definite problem in mind which narrows the field 
of attention. This is one of the reasons why experi- 
mentation is so satisfactory. 

Another condition of good observation is the posses- 
sion of good mental habits. He who is on his guard 
against the influences constantly at work to distort ob- 
servation is more apt to observe correctly. He will try 
to keep his mind open, to thrust prejudices and pre- 
conceptions aside, to allow facts repugnant to him, for 
one reason or another, as much weight as favorable facts ; 
in short, he will try to keep his mind as receptive to all 
relevant facts as he is able. This neutrality of mind is 
harder to attain to than is generally supposed. It is an 
achievement of training and education. 

Errors in Perception. Errors in perception are 
usually classified under two headings, ; mal-observation ' 



188 THE ESSENTIALS OF LOGIC 

and ' non-observation/ Mal-observation is, again, of two 
kinds : addition to what is present and wrong arrange- 
ment of the parts. Non-observation is essentially omis- 
sion. Let us consider these types of perceptual error 
in some detail. 

We constantly add elements to interpret or enlarge 
what we actually perceive. This is not surprising when 
we remember that sensation is only a small part of per- 
ception. Association and suggestion are fundamental 
factors in perception, and we see what we wish to see 
or expect to see so long as the sense-factors and the 
general situation do not forbid us. When common sense 
says that seeing is believing, it is not aware of the part 
played by past experience and by desire in what we 
ordinarily take to be given. And this ignorance that 
perception is a product accounts for the dogmatism of 
common sense and for its perplexity when confronted 
by varying stories of the same events. In his book en- 
titled On the Witness Stand, Professor Miinsterberg 
illustrates the influence of mental factors in perception 
by the following instances : " In some Bowery wrangle, 
one witness was quite certain a rowdy had taken a beer- 
mug and kept it in his fist while he beat with it the 
skull of his comrade ; while others saw that the two 
were separated by a long table, and that the assailant 
used the mug as a missile, throwing it a distance of six 
or eight feet. In another trial, one witness noticed at 
the seashore in moonlight a woman with a child, while 
another witness was not less sure that it was a man 
with a dog. And only recently passengers in a train 
which passed a courtyard were sure, and swore, that 
they had taken in at a glance the distinct picture of a 



OBSERVATION AND FACT 189 

man whipping a child ; one swore that he had a clean- 
shaven face, a hat, and was standing, while another 
swore that he had a full beard, no hat, and was sitting 
on a bench. The other day two most reliable expert 
shorthand writers felt sure that they heard the utterances 
which they wrote down, and yet the records differed 
widely in important points." 

Non-observation is the overlooking of facts which 
ought to be observed. "It is exceeding rare to find 
persons who can with perfect fairness estimate and reg- 
ister facts for and against their own peculiar views and 
theories. Among uncultivated observers the tendency 
to remark favorable and forget unfavorable events is 
so great that no reliance can be placed upon their sup- 
posed observations. Thence arises the enduring fallacy 
that the changes of the weather coincide in some way 
or other with the changes of the moon, although exact 
and impartial registers give no countenance to the fact. 
The whole race of prophets and quacks live upon the 
overwhelming effect of one success, compared with 
hundreds of failures which are unmentioned and for- 
gotten. As Bacon says, ' Men mark when they hit, and 
never mark when they miss.' We should do well to 
bear in mind the ancient story, quoted by Bacon, of one 
who in pagan times was shown a temple with a picture 
of all the persons who had been saved from shipwreck, 
after paying their vows. When asked whether he did 
not now acknowledge the power of the gods, ' Aye,' 
he answered, ' but where are they painted that were 
drowned after their vows ? * " x 

Causes of Erroneous Perception. A helpful 

1 Jevons, The Principles of Science, vol. n, p. 5. 



190 THE ESSENTIALS OF LOGIC 

classification of the causes of erroneous perception is 
into physical, physiological, and psychological. 

Physical conditions are very important for correct 
observation. When the atmosphere is unclear, the sci- 
entist does not ; make observations,' for he knows that his 
data will be faulty. But since we are as much concerned 
with everyday reasoning as with science, w r e must note 
some of the difficulties due to external conditions. Ob- 
jects change their colors according to the source of illu- 
mination. In a fog, objects look immense because our 
ordinary standards are removed. The dweller in the plain 
is unable for a long time to estimate distances in a 
mountainous region correctly. On the more technical 
side, we may mention the fact that instruments affect 
perception in various ways. Unless these sources of 
change are recognized and met, the data obtained may 
be misleading. 

Physiological conditions are likewise important. 
Taste and color are affected by the condition of the 
body. Again, the registration of flashes of light in their 
time-relations cannot be made by perception because of 
a certain inertia in the nervous system. A glare of 
light is necessarily seen some fraction of a second aftSHP 
the eye has been stimulated. In delicate scientific work, 
the part played by the organism in perception is taken 
account of and automatic registrations are employed 
wherever possible. 

Psychological factors are of more importance, but, 
since we have made some mention of them already, we 
will not dwell upon the topic. Misplaced attention leads 
to faulty observation. This cause is important in the 
activity of the prestidigitator, the false medium, the 



OBSERVATION AND FACT 191 

pickpocket ; they direct the attention of their subjects 
away from what is actually of most importance to 
them. Another instance of the significance of the psy- 
chological element is the value of training in the use 
of instruments such as the microscope. Again, the mind 
is affected by bad health. There is not the same possi- 
bility of controlled and tireless attention under abnor- 
mal conditions, however induced. An individual must 
be physically and mentally fit to be in a good condition 
for observation. 

Summary for Perception. Seeing is not the sim- 
ple and direct operation so often assumed. It has its 
conditions, physical, physiological, and psychological. 
Of these, the psychological are of the greatest impor- 
tance for everyday life. Association and past experi- 
ence in general play into perception, and its direction 
and content are determined by interest, desire, and 
other obscurer factors. Consequently, perception, even, 
cannot be taken at its face value when much is at 
stake ; it must be tested and, if possible, repeated. We 
see much less than we suppose, and that is why obser- 
vation is fullest when we have a definite purpose. 

Observation in Everyday Life and in Science. 
Because the scientist has become aware of these dangers, 
he has made observation a more careful and intelligent 
operation than it is in everyday life. The scientist 
makes an observation. He knows what he is about 
and guards against dangers so far as possible. One ad- 
vantage he usually has is that his observations can be 
repeated. An individual who is called before a court 
as a witness is only too painfully conscious that he did 
not know just what to observe ; his attention was too 



192 THE ESSENTIALS OF LOGIC 

diffused and unguided to give definite results. He has, 
moreover, no records and must trust to memory with 
its attendant errors. 

Memory and Facts. Memory is selective much 
as perception is. We are likely to remember only 
those events which w r e have expressly attended to ; 
and a further elimination comes from the fact that 
we are much more apt to remember favorable than un- 
favorable things. This tendency to forget what is 
unpleasant was recognized by Darwin. "I had also," 
he writes, " during many years, followed a golden rule 
— namely, whenever a published fact, a new observa- 
tion or thought came across me, which was opposed to 
my general results, to make a memorandum of it with- 
out fail and at once ; for I had found by experience 
that such facts and thoughts were far more apt to 
escape from the memory than favorable ones. Owing 
to this habit, very few objections were raised against 
my views which I had not at least noticed and at- 
tempted to answer." 1 

Habits of mind or customary points of view furnish 
the centers for this unconscious selection. Events which 
cannot be made to fit into the scheme of values and 
ideas which is gradually established in the personality 
drop into the background and finally cease to appear 
in consciousness. Not only is there omission, there is 
also distortion and coloring of what is remembered. 
A person who writes his autobiography is apt to dis- 
tort the facts of his life. That is why such narra- 
tives must always be checked where possible by ex- 
ternal evidence. We must not say that Wagner and 

1 Autobiography, p. 87. 



OBSERVATION AND FACT 193 

Disraeli lied, they simply deceived themselves. Who, 
moreover, can be perfectly frank, even to himself, 
about himself? Inhibitions of various sorts and our 
dramatic sense are at work upon the materials of our 
past life to make them more presentable. 

Summary of Causes of Mistaken Memory. The 
following summary of the causes of mistaken memory 
may be helpful : — 

We tend to remember what has usually happened 
and to forget the exceptional unless it is very striking. 

We tend to remember events which are pleasant 
and fit in with the general trend of our lives and the 
drift of our ideas. 

We tend to remember the heights and depths and 
to allow the more colorless events to lapse. 

We tend to dramatize and develop events by an un- 
conscious process of construction and inference. 

The logician is aware that memory is not an intui- 
tion but a product, and that it must be tested by its 
inner consistency and by means of external evidence. 
The shorter the time which has elapsed, the more 
truthful it is found to be. 

Testimony. Testimony is a still more indirect source 
of knowledge than memory. When we ourselves have 
not been the witnesses of an occurrence, we are com- 
pelled to have recourse to the statements of eye-wit- 
nesses. But a double danger of error is now present. 
We must be certain that those who claim to be were 
actually witnesses at first hand. Even so, they were sub- 
ject to all the causes of mal-observation which we have 
already stressed, and, added to this, is the liability to 
change which their testimony is subject to in its passage 



194 THE ESSENTIALS OF LOGIC 

to our minds. Mal-observation, fallacious memory, in- 
accurate expression, misinterpretation, this is the series 
of distorting tendencies which makes ' fact ' always 
more or less hypothetical. The consequence is that 
such tentative facts must be carefully examined before 
they are accepted. Methodical tests must be worked 
out and carefully applied ; it is not too much to say 
that facts are critical judgments rather than something 
passively given. 

Facts differ in Different Sciences. The data to 
which the investigator must adhere in his achievement 
of systematic knowledge vary from science to science. 
It is very important to bear this in mind, for, other- 
wise, it is impossible to understand differences in the 
methodology and technique of these various sciences. 
Inductive logic cannot be formal to the same extent 
that the logic of consistency is able to be. The geo- 
metrician secures his data by means of axioms and 
postulates which seem to him self -consistent, and which 
he relates to a spatial system lending itself to construc- 
tion and manipulation. His methods reflect this founda- 
tion and are dominantly inspectional and deductive. 
The physical sciences obtain their data by active ob- 
servation aided by experimentation. These observations 
lend themselves to repetition. The historical and social 
sciences have more difficulty in securing their data ; in 
fact, data are more the end-terms of their investiga- 
tions than the beginning. In their cases, we must dis- 
tinguish between the crude material with which they 
start and the conclusions upon which they base their 
final interpretations. Between these stages lies a per- 
fected technique of criticism and analysis. Thus the 



OBSERVATION AND FACT 195 

character of investigation is modified by the nature of 
the problem, the aim of the investigator, and the kind 
of knowledge achieved. In spite of this variation, there 
is, however, the constant presence of the three elements 
to which we referred in the chapter introductory to 
this part of logic. There must be observation and col- 
lection of data, conjecture, systematic reasoning about 
the conjecture, and, finally, a return to observation. 
Only as the result of such systematic inference can 
knowledge be achieved. 

What are Relevant Facts? We speak of the 
facts of a case and of relevant facts ; how do we know 
what facts are relevant and what facts do actually be- 
long to the case ? They do not come labeled nor is the 
degree of their importance visibly stamped upon them. 
A prime condition of the acquisition of essential facts 
is guidance by some idea. We must know what we 
want, must have insight, judgment, discernment. Such 
discernment is, in part, the effect of familiarity with 
the field. The expert knows what to look for ; he is 
able to narrow down the search to data of a certain 
character. There is in this sense of location what the 
psychologist calls an apperceptive or deductive element. 
Past experience is funded. We see and judge with the 
mind. Strictly speaking, there is no such thing as 
purely passive observation. There is usually a decid- 
edly purposive factor at work. Guesses and conjectures 
arise to guide the direction in which to look for evi- 
dence. Especially is this the case when resort is had 
to experimentation. We may say, then, that all obser- 
vation involves the selection of what is thought to be 
essential. The mind picks from the crowd of facts press- 



196 THE ESSENTIALS OF LOGIC 

ing upon attention those which are judged to be rele- 
vant. In other words, observation is in the service of a 
continuous process of interpretation and judgment. 



REFERENCES 

Bode, An Outline of Logic, chap. xiii. 
Gibson, The Problem of Logic, chap. xiii. 
Jevons, Lessons in Logic, chap. xxvn. 
Jones, Logic, Inductive and Deductive, chap. II. 
Sidgwick, The Process of Argument, chap. vin. 



CHAPTER XVIII 

THE ORIGIN AND USE OF HYPOTHESES 

What is an Hypothesis? An hypothesis is any 
conception by which the mind goes beyond the known 
facts and seeks to establish relations between data of 
testimony and perception, so long as that conception 
is one among alternative possibilities and is not con- 
sidered a fact. This definition, adapted from Bosan- 
quet's larger Logic, brings out the essential position of 
an hypothesis as between accepted fact and accepted 
theory. It is a conjecture, a guess, a provisional expla- 
nation. Just because an hypothesis is conjectural, it is 
primarily a mental contribution whose aim is the solu- 
tion of some problem. It is an interpretation or en- 
largement of what is given. 

As a tentative solution of a problem, an hypothesis 
is an idea held before the mind in answer to a purpose, 
that of explanation. But this purpose cannot be ful- 
filled until many further steps are taken. The implica- 
tions of the conjecture must be reasoned out and the 
attempt made to bring them into touch with a com- 
pleter survey of the facts. Hence, a genuine hypothesis 
arises in fact and keeps in touch with fact throughout 
its history. Because of this continuous responsibility 
to, and control by, fact, the conjectural stage in inves- 
tigation does not sin against the inductive principle of 
Fidelity to Fact. All that must be guarded against is 
that dreamy sort of speculation which soars into the 



198 THE ESSENTIALS OF LOGIC 

heavens and never seeks to return. " The truly scien- 
tific thinker has none of the spirit which says, ' If the 
facts do not agree with the theory, so much the worse 
for the facts.' " 1 

Kinds of Hypotheses. The nature of a particular 
hypothesis depends upon the character of the problem 
for which it is a tentative answer. Sometimes we are 
on the lookout for a fact, as when we are in search for 
a particular cause of an occurrence like a fire or a 
crime ; sometimes we wish to establish a law of nature, 
such as a law of physical chemistry ; sometimes we de- 
sire to conceive the structure of an empirical substance 
like rubber or protoplasm ; sometimes we are pressing 
forward to some immense generalization like the prin- 
ciple of the conservation of energy or the theory of 
evolution. In each case, the mind must suggest ideas 
and then seek to establish them. The nature of the 
problem determines the character of the explanatory 
conjecture. 

Are Hypotheses necessary for Science? At 
various times in its history, science has been skeptical 
of the necessity and even of the value of hypotheses. 
During such periods, the ideal is to let facts speak for 
themselves. It is supposed that, if facts enough are 
collected and tabulated, the principle which is sought 
will somehow stand out from them and force itself on 
the attention. " The natural goal of science based on 
this radically empirical method is to become a Science 
of Statistics so compiled and arranged as to force upon 
the methodical collector of observations the laws which 
the facts require to explain them. In this way, labori- 
1 Welton, Manual of Logic, vol. n, p. 86. 



THE ORIGIN AND USE OF HYPOTHESES 199 

ous method takes the place of the scientific imagination 
and the happy idea." 1 This way of approach is often 
called the ' Baconian method ' after Francis Bacon, one 
of the founders of modern logic. It represents a pro- 
test against an overspeculative tendency not fed on 
facts. It is, however, itself obviously another extreme. 
The relative importance of theory and fact varies from 
time to time and from subject to subject. It is now 
pretty generally held that the situation controls the 
amount of conjecture, but that a free play of the mind 
must always be present. It is psychologically impos- 
sible for principles to arise from facts without the col- 
laboration of the mind. Neither observation nor concep- 
tion is a passive event. Science is not a mere collection 
of facts. 

A brilliant group of men who were at once scientists 
of recognized rank and thinkers championed the cause 
of hypotheses during the latter part of the nineteenth 
century, and their vindication of the controlled use of 
hypotheses has won general acceptance. These men 
worked in both the physical and the biological sciences. 
The following quotation from Huxley is typical : " It 
is a favorite popular delusion that the scientific inquirer 
is under a sort of moral obligation to abstain from going 
beyond that generalization of observed facts which is 
absurdly called ' Baconian ' induction. But any one who 
is practically acquainted with scientific work is aware 
that those who refuse to go beyond fact rarely get as far 
as fact ; and any one who has studied the history of science 
knows that almost every great step therein has been 
made by 4 anticipation of nature,' that is, by the inven- 
1 Gibson, The Problem of Logic, p. 313. 



200 THE ESSENTIALS OF LOGIC 

tion of hypotheses which, though verifiable, often had 
little foundation to start with, and not infrequently, in 
spite of a long career of usefulness, turned out to be 
wholly erroneous in the long run." 2 

The Origin of Hypotheses. There are at least two 
conditions leading to the formation of hypotheses, the 
possession of facts bearing upon a problem and mental 
spontaneity. There is a constant interaction between 
these two factors the one creative and the other con- 
trolling and suggestive. As a rule, an hypothesis is not 
a sudden intuition, but a mental growth which matures 
in the fertile soil of accurate and extensive knowledge. 
When the history of any progressive investigation is 
written, analysis shows that there is a continuous trans- 
verse movement between data and conjecture. Conjecture 
guides observation and experimentation while the results 
of such further observation modify conjectures and se- 
lect among them. We must always remember that the 
steps of induction which the logician separates out for 
study do not exist separately as mutually exclusive stages. 

There is pretty general agreement that fruitful hy- 
potheses are creations of constructive imagination. In 
its higher levels, such constructive imagination is a rare 
gift. A great scientist must combine many capacities ; 
he must be a tireless observer and classifier ; he must 
be able to organize his material and include it in one 
comprehensive survey ; but he must also be able to seize 
that idea which will illuminate it and give it life and 
meaning. Tyndall was aware of the importance of this 
more personal factor of imaginative interpretation when 
he wrote : " With accurate experiment and observation 
1 Methods and Results, p. 62. 



THE ORIGIN AND USE OF HYPOTHESES 201 

to work upon, Imagination becomes the architect of 
physical theory. Newton's passage from a falling apple 
to a falling moon was an act of the prepared imagina- 
tion, without which the ' laws of Kepler ' could never 
have been traced to their foundations. Out of the facts 
of chemistry the constructive imagination of Dalton 
formed the atomic theory. Davy was richly endowed 
with the imaginative faculty, while with Faraday its 
exercise was incessant, preceding, accompanying, and 
guiding all his experiments. His strength and fertility 
as a discoverer is to be referred in great part to the 
stimulus of his imagination. Scientific men fight shy of 
the word because of its ultra-scientific connotations ; but 
the fact is, that, without the exercise of this power, our 
knowledge of nature would be a mere tabulation of co- 
existences and sequences." l 

A G-lance at the Psychology of Conjecture. The 
form of scientific imagination varies with the nature of 
the science. " No one will question that mathematicians 
have a way of thinking all their own ; but even this is too 
general. The arithmetician, the algebraist, and more 
generally the analyst, in whom invention obtains in the 
most abstract form of discontinuous functions — sym- 
bols and their relations — cannot imagine like the 
geometrician." 2 The case seems to be that the nature 
of the materials is a factor of first importance ; it is deter- 
mining, and indicates to the mind the direction in which 
it is turned. Furthermore, some individuals are better 
able, by the very constitution of their minds, to work 
in a certain kind of material than in other kinds. Again, 

1 Fragments of Science, pp. 111-12. 

2 Ribot, Essay on the Creative Imagination, p. 237. 



202 THE ESSENTIALS OF LOGIC 

there are distinct differences in type when we come to 
consider the way in which the illuminating idea arrives. 
Roughly speaking, there are two types of creative minds, 
the intuitive and the reflective. 

With the intuitive mind, the preparation is largely 
unconscious. The illuminating idea, when it does come, 
seems to burst upon the individual like a stroke of in- 
spiration. There is a cry of 'Eureka' and the new view 
is born. Musicians and poets are more likely to have this 
type of creative imagination than are scientists; yet 
" Hauy drops a bit of crystallized calcium spar, and, 
looking at one of the broken prisms, cries out, * All is 
found ! ' and immediately verifies his quick intuition in 
regard to the nature of crystallization." * 

The reflective mind, on the other hand, realizes that 
there is a problem to solve and approaches its solution 
systematically. Such an individual gathers his material 
and broods over it. An interpretative idea gradually 
forms itself and is developed little by little. Perhaps it 
is soon rejected, and another grows up to supply its 
place. Kepler is a good example of the reflective mind. 
He devoted a large part of his life to trying new and 
strange hypotheses about the planetary movements until 
the day he discovered the elliptical orbit of Mars. 

According to Ribot, the differences between these 
two types of minds are largely reducible to temperament 
and disposition. He works out the contrast as follows : — 

Intuitive type Reflective type 

Ready-witted minds, excelling in Logically developing minds, 
conception, making the whole excelling in elaboration, 
almost out of one piece. 

1 Ribot, Essay on the Creative Imagination, p. 247. 



THE ORIGIN AND USE OF HYPOTHESES 203 

Intuitive type Reflective type 

Work primarily unconscious. Patience the preponderating 

role. 
Work primarily conscious. 
Actions quick. Actions slow. 

When we contrast these two types of mind, it be- 
comes evident that logic has more to learn from, and 
more to convey to, the reflective type. But we must not 
forget that in any complex field of investigation to-day, 
the contrast is quite relative. There must always be 
patience and conscious effort. 

Running all through logic is an almost moral ele- 
ment. The history of investigation proves that certain 
attitudes are favorable to invention and discovery while 
others are distinctly unfavorable. Creative imagination 
does not exist in a mind that is conventional and domi- 
nated by habit and routine. " Alertness, flexibility, cu- 
riosity, are the essentials ; dogmatism, rigidity, prejudice, 
caprice, arising from routine, passion, and flippancy 
are fatal." l 

The Value of Hypotheses. We have already said 
enough to indicate wherein the value of an hypothesis 
lies. It sharpens and guides the mental eye. The fol- 
lowing anecdote from the life of Darwin brings out this 
feature very well : " Darwin tells of a geological trip 
through Wales which he took while a student at Cam- 
bridge, in company with Sedgwick, the professor of 
geology. It must be remembered that this was before 
Agassiz had come forward with his theory of a glacial 
period in the world's history. Darwin writes : ' We 
spent many hours in Cwm Idwal, examining all the 
1 Dewey, How We Think, pp. 105-06. 



204 THE ESSENTIALS OF LOGIC 

rocks with supreme care, as Sedgwick was anxious to 
find fossils in them ; but neither of us saw a trace of 
the wonderful glacial phenomena all around us ; we did 
not notice the plainly scored rocks, the perched bould- 
ers, the lateral and terminal moraines. Yet the phe- 
nomena are so conspicuous that, as I declared in a paper 
published many years afterward in the Philosophical 
Magazine, a house burnt down by fire did not tell its 
story more plainly than did this valley. If it had been 
filled by a glacier, the phenomena would have been less 
distinct than they are now.' ,?1 As James put it, " The 
only things which we commonly see are those which we 
pre-perceive." 

But an hypothesis is of value also because it begins 
a systematic analysis and synthesis of the facts. It is 
the beginning of an explanatory view which seeks to 
penetrate below appearances to the causes at work and 
their structure. When verified, hypotheses become the- 
ories and so enter as substantial elements in our knowl- 
edge of the world. 

It is now generally admitted that an hypothesis 
which afterwards turns out to be false may have justi- 
fied itself in a measure by its serviceableness. It is a 
nice question whether this relative serviceableness can 
be connected with an element of truth in its constitu- 
tion or whether it is due to the guidance which it exer- 
cises. Any conjecture exerts a steadying control on 
attention and encourages the collection of facts, some 
of which may lead to its own dethronement. We must 
not forget, however, that an accepted hypothesis may 
prevent the consideration of truer ones and may in 
1 Life and Letters of Charles Darwin, quoted from Creighton. 



THE ORIGIN AND USE OF HYPOTHESES 205 

this way retard progress. Certainly it is better to deal 
with true hypotheses than wiih erroneous ones. The 
Ptolemaic Hypothesis and the^Newtonian Corpuscular 
Theory of Light are famous examples of long accepted 
hypotheses which were finally rejected. 

The danger in the use of hypotheses is due to the 
tendency to dogmatism. All scientists are liable to 
"the partiality of intellectual parentage." One way to 
counteract this latent dogmatism which blinds the men- 
tal vision is to become conversant with the history of 
the various sciences. When we see theory succeed the- 
ory and even those which have stood the acid test of 
years of investigation modified in more or less essential 
points, we are less apt to retain our primitive assertive- 
ness. Another way to prevent dogmatism is to keep 
before the mind at one and the same time a number of 
rival hypotheses. This is called the ' Method of Multiple 
Working Hypotheses.' 

The Development of an Hypothesis. An hy- 
pothesis is barren which cannot be so developed as to 
imply verifiable consequences. The development of an 
hypothesis is sometimes called ' reasoning,' sometimes 
1 deduction.' What we do is to work out its conse- 
quences in the light of our knowledge of the system in- 
volved. Ideas which at first glance seemed plausible 
frequently turn out to be quite impossible. This maul- 
ing-over of ideas to get their bearings is essential. Let 
me first take a very simple case to illustrate the 
method. I see footprints on the beds in the garden 
which I have just planted. The idea comes to me that 
my young son has been disobeying my injunctions. But 
if these are his footprints, they will be only so large. I 



206 THE ESSENTIALS OF LOGIC 

look more closely and discover that they are larger. 
Thus my hypothesis has been developed and tested. 
This same process is apparent in all cases of reasoning. 
Detective stories are full of rather artificial examples 
of developed guesses which are valid or invalid as the 
case may be. 

Science is replete with hypotheses which have lent 
themselves to development. Thus, Torricelli's theory 
that the air has weight implied that heavier liquids 
would not be raised so high in a vacuum as lighter 
liquids. This implication was tested and found to hold. 
Another implication was that the mercury would not 
stand so high on a mountain as on a plain. This also was 
verified. The implications of an idea can often be worked 
out only by one who is cognizant with the whole system 
of relations and facts within which the idea must fit. 
Thus, Foucault showed that it takes longer for light to 
travel in a dense medium than in a rare medium. But 
the Corpuscular Theory of Newton had the reverse of 
this for its implication, and was therefore disproved. 
The general form of reasoning about an idea is hypo- 
thetical : if this is so, then this other is so ; but if this 
other is so, then this fact follows. The chain may be 
short or long, but it must eventually end in a datum 
theoretically open to observation. 

The Proof of an Hypothesis. A distinction must 
be made between verifying an hypothesis and proving 
it. An hypothesis is verified so far as its logical conse- 
quences in the system of knowledge of which it claims 
to be part are harmonious with the facts. 4 If A is By 
we may decide, ' then C is DS We observe with or 
without experimentation and discover that C is D. 



THE ORIGIN AND USE OF HYPOTHESES 207 

This agreement reinforces our inclination for the posi- 
tion that A is B. So long as there is no other claimant, 
we tend to regard the conjecture as true. It cannot, 
however, he said to be proved in any final sense until 
it can be shown that no other hypothesis can account 
for the facts. The logical situation involves the princi- 
ple of the hypothetical syllogism. It will be remem- 
bered that it is impossible to affirm the consequent and 
draw a certainly valid conclusion. Because C is D, it 
does not follow that A is B. But it is impossible to 
eliminate all other possible theories because we can 
never be certain of working within a complete disjunc- 
tion. What, then, determines our confidence in a suc- 
cessful hypothesis ? Ultimately a consilience of results. 
When a very large field is covered and coordinated by 
a conjecture and no other plausible idea is in sight or 
seems likely to be advanced, we give our assent and 
regard the hypothesis as proved. 

Fact, Theory, and Hypothesis. Facts are of two 
kinds, facts of observation and facts of belief. While 
it must not be forgotten that even facts of observation 
are really statements which are open to reasonable 
doubt, the judgments and tests involved are usually 
simpler than for the second kind of facts. This second 
class of facts are complex statements which have 
reached the stage of practical certainty. They are far- 
ther away from perception than the first and involve 
conceptual construction of an advanced degree. It is a 
fact of observation that a stick seems bent in the water, 
but a fact of assent that the earth revolves around the 
sun. Both classes have this in common that we give 
their members whole-hearted belief. 



208 THE ESSENTIALS OF LOGIC 

When an idea is first suggested and entertained by 
the mind, it is called an * hypothesis.' When its conse- 
quences are deduced and verified, it is apt to be digni- 
fied by the name of i theory.' When it has gained un- 
questioned acceptance, it is likely to be spoken of as a 
4 fact ' or a ' principle.' Not so long ago, evolution was 
referred to as an hypothesis ; then it became a theory ; 
now it has attained the standing of a fact or a princi- 
ple. We must remember that there is no court of adju- 
dication, so that what is a principle to one may be an 
hypothesis to another. 

Analogy as a Basis of Reasoning. The remark 
is often made that such-and-such a conclusion was 
reached by analogy. We admittedly reason by analogy 
from one field to another. Examining such reasoning, 
logicians point out that it consists of the passage from 
one thing or group of things to another because of a 
recognized resemblance between them. " Two things 
resemble each other in one or more respects ; a certain 
proposition is true of one, therefore it is true of the 
other." * Now such a passage is usually tentative and 
is therefore of the nature of ah hypothesis ; this fact is 
our justification for treating the topic in this chapter. 

The symbolic form of analogy is as follows : A re- 
sembles B in certain respects ; A exhibits the charac- 
ter V) therefore B will exhibit the character "Falso. In 
other words, we tend to hold that if two things agree in 
certain respects they are apt to agree in others. All 
classification is really based on analogy in this broad 
sense; but in classification the similarities noted are 
many and fundamental and we are dealing with what 
1 Mill, System of Logic, bk. in, chap, xx, par. 2. 



THE ORIGIN AND USE OF HYPOTHESES 209 

we have reason to believe are things of the same kind. 
There is, however, no decided break between what is 
clearly classification and what would be admitted by all 
to be mere analogy. " Where analogy is very close, and 
well tested, and familiar, as between cancer and cancer, 
or man and man, class-names have generally been in- 
vented. It is newly seen likeness, doubtful likeness, or 
likeness where the examples are rare, that we have to 
recognize as well as we can without the aid of class- 
names. And it is to these kinds of likeness especially 
that, as a rule, we give the name ' analogy.' " 1 It is 
not too much to say that all the reasoning in a new 
field bases itself upon analogies with more familiar do- 
mains. Thus the wave character of the propagation of 
light was inferred from the known fact that sound 
which also was reflected traveled in waves. 

False Analogy. Analogies are very apt to be mis- 
leading. After all, things may be similar in this respect 
or that while differing in almost everything else. The 
points of similarity are often superficial and not corre- 
lated with the properties which are important for the 
problem in hand. Because a whale lives in the water 
and is shaped very much like a fish, it does not follow 
— as was at one time supposed — that it has the deeper 
structure of a fish. Because a municipality is a gov- 
ernment, it does not follow that it must have the same 
type of organization as the Federal Government. An 
argument from analogy has a high degree of probabil- 
ity only when the points of resemblance are rooted deep 
in the nature of the two things and there is reason to 
believe that in the familiar field there is a connection 

1 Sidgwick, The Process of Argument, p. 40. 



210 THE ESSENTIALS OF LOGIC 

between the points of resemblance and the property 
which we wish to infer in the new field. A good in- 
stance of what must be regarded as a false analogy is 
Carlyle's argument against the representative form of 
government. " According to Carlyle, this kind of gov- 
ernment is bound to fail, since, as he puts it, a ship 
could never be taken around Cape Horn if the captain 
were obliged to consult the crew every time before 
changing his course. A generalization is implied, some- 
thing like, 4 The sharing of power involves a lack .of 
efficiency.' Granted that this holds true on ships, is it 
also true in government ? The argument asserts that 
the two cases are alike, but it offers no proof that the 
difference in circumstances is immaterial. The appar- 
ent difference, however, is so great that caution is ad- 
visable. It may be that the lack of efficiency is due to 
the sharing of power under certain conditions peculiar 
to the management of ships." 1 

It is obvious that analogy must be controlled by anal- 
ysis. False analogies always rest upon the disregard of 
differences. Thus analogy is a fruitful source of sug- 
gestions but these must be tested by a further survey 
of the facts and an estimation of their meaning. Re- 
semblance may, as the saying goes, be only skin deep. 

REFERENCES 

Bode, An Outline of Logic, chap. XX. 
Joseph, An Introduction to Logic, chap. xxiv. 
Ribot, Essay on the Creative Imagination, chap. IV. 
Sidgwick, The Process of Argument, chap. IV. 
Welton, Manual of Logic, vol. n, chaps, in and IV. 

1 Bode, An Outline of Logic, p, 163. 



CHAPTER XIX 

THE DISCOVERY AND PROOF OF CAUSAL RELATIONS 

How Experience comes to us. The individual's 
experience comes to him in an accidental, haphazard 
way, and it is only as the result of unconscious or 
semiconscious sorting and generalization that he re- 
duces it to some show of order. Things are recognized 
and classified into kinds, and these kinds are supposed 
to have certain properties which can be predicted 
and counted on. Iron is malleable ; coal burns ; swans 
are white; apple trees yield apples after their kind, 
etc. By means of these classifications and generaliza- 
tions, we are able to handle things and adapt ourselves 
to our environment. 

But there is another feature of our experience which 
is equally important. We soon learn to note that 
events in which we are interested are controlled bv 
conditions. If we want B to happen, we must see that 
A is added. If we want the garden to produce an 
abundant crop, we must add fertilizer in the proper 
proportions. If the manufacturer wishes to have steel 
of a certain degree of hardness, he must add manga- 
nese. When any factor is known to be an invariable 
antecedent of some event or situation, and it is also 
known that this event does not occur in the absence of 
this factor, it is called a cause. Such a cause is a 
means to an end, and is of practical significance. If 
we wish to achieve any result, we must see that all the 
conditions are present. 



212 THE ESSENTIALS OF LOGIC 

What are Causal Connections ? It is usually 
said that science deals with the causes of things. What 
is meant by this expression ? And what is a cause ? A 
little reflection warns us that, because we are studying 
the actual methods of science, we have to do with a 
purely empirical problem. What the scientist is search- 
ing for is the condition of changes. Something hap- 
pens, and he wants to know why* He is on the outlook 
for the factor which has led to the change in which he 
is interested. As soon as I add sulphuric acid to the 
test-tube which I hold in my hand, I begin to get a 
reaction, and I soon see a deposit at the bottom of the 
tube. Cause has, in short, to do with change in vari- 
ous parts of nature. We desire to know what disturbs 
the previous equilibrium and thus leads to novelty. A 
cause is, then, a factor which, so far as we can deter- 
mine, is the occasion of the event which is selected as 
the effect. 

When we come to reflect upon the relation between 
a cause and its effect, we note at once its temporal 
character. The entrance of the causal factor is the an- 
tecedent of the effect. But we are not willing to con- 
sider the entering factor a cause unless its absence 
involves the absence of the effect. It must be an indis- 
pensable antecedent. And it is not always easy to 
decide what factor is indispensable. We must know 
enough about the field to make a good guess or guesses, 
and we must then experiment to find out whether a 
fuller knowledge agrees with the guess. 
^Post Hoc ergo Propter Hoc. Even the older logi- 
cians were perfectly aware of the danger of false gen- 
eralization. Because one event precedes another, we 



CAUSAL RELATIONS 213 

must not jump to the conclusion that they are caus- 
ally related. If we take the antecedent of an event in 
a purely temporal way, it includes the whole range of 
occurrences which can be dated before the event which 
we are interested in. A causal relation involves more 
than this temporal antecedence; it implies conviction 
that certain specific events located in some definite 
part of space are most intimately connected with the 
effect. He who is on the outlook for causal relations 
is seeking special strands of connection. He wants to 
find constantly repeated, invariable, dependable connec- 
tions. His ideal is to analyze nature into uniformities 
which can be made the basis of prediction and control. 

Early man had much the same tendency to treat 
temporal relations as causal that we have to-day, but 
he was far more credulous and hasty in his generaliza- 
tions. What we call superstition and magic consisted 
largely of uncritical beliefs of this character. Chance 
association by contiguity or likeness was the founda- 
tion of accepted laws. The mind was ruled by ideas 
and made its selections accordingly with practically no 
thought of verification. It seemed very likely that the 
eating of a lion's heart would supply courage to the 
warrior ; and had not B been unlucky when a rabbit 
crossed his path ? The selection among events was per- 
sonal and controlled by chance ideas and associations. 
To the critic the reply would have been, Why not? 
And there was a dearth of critics. It took time and 
hard experience to produce them. 

The tendency to regard events as causally related 
just because one has been observed to follow the other 
has been christened ' Post Hoc ergo Propter Hoc? 



214 THE ESSENTIALS OF LOGIC 

i.e., * After, therefore, Because of.' " The history of the 
progress of human knowledge shows, with increasing 
clearness, that better solutions are given in proportion 
as we recognize our own liability to be misled by first 
appearances. It is the testing and verification of 
theories, not the easy belief that they need no testing, 
that helps forward our knowledge of the ways of 
Nature." 1 

Mill's Methods. The human mind has gradually 
hit upon methods for discovering and testing causal 
relations. These were first sensed in the concrete by 
scientists in the pursuit of particular problems and 
were formulated some time after when reflection upon 
the general methods employed had arisen. The meth- 
ods for determining causal relations were partially 
formulated by Herschel in his Discourse on the Study 
of Natural Philosophy, and were given their nearly 
final form by John Stuart Mill. For this reason, they 
are usually spoken of as 4 Mill's Methods.' How can 
causal generalizations be discovered and verified ? This 
is the problem around which they turn. 

Mill formulated five methods, but the principles in- 
volved are essentially two. " The simplest and most 
obvious modes of singling out from among the circum- 
stances which precede or follow a phenomenon (any 
event), those with which it is really connected by an 
invariable law, are two in number. One is by com- 
paring together different instances in which the phe- 
nomenon occurs. The other is by comparing instances 
in which the phenomenon does occur, with instances in 
other respects similar in which it does not. These two 

1 Sidgwick, The Process of Argument, pp. 132-33. 



CAUSAL RELATIONS 215 

methods may be respectively denominated the i Method 
of Agreement ' and ' Method of Difference.' " These 
two principles would seem to follow from the very nature 
of the causal relation. If a cause is the indispensable 
antecedent of a phenomenon, can we not conclude (1) 
that the antecedent in the absence of which the phe- 
nomenon occurs is not the cause, and (2) that the ante- 
cedent in whose presence the phenomenon fails to occur 
is not the cause ? It would seem possible, therefore, to 
eliminate factors which are absent when a particular 
effect occurs and to test those which remain by seeing 
whether their absence involves the absence of the effect. 
In this way, resort can be made to experimentation. 

The Method of Agreement. " If two or more 
instances of the phenomenon under investigation have 
only one circumstance in common^ the circumstance in 
which alone all the instances agree is the cause (or 
effect) of the given phenomenon" Such is Mill's state- 
ment of the Canon of Agreement. It is possible to 
represent this canon schematically. Let X be the 
effect whose cause we wish to find, and let the accompa- 
nying circumstances be represented by abcde, afklm, and 
aghno in three cases of the appearance of the effect. 
Putting down these groups in the above order, we have : — 

ahcdeX 
qfklmX 
aghnoX. 

Comparing these groups, we see that a is the sole factor 
which always accompanies X, and hence we feel the 
right to conclude that a is the cause of X. 

Such a schematic arrangement, while it illustrates the 



216 THE ESSENTIALS OF LOGIC 

canon, is apt to be misleading because of its simplicity 
and artificiality. Much of the work of investigation 
must be done before any such neat little scheme can be 
constructed. But, after all, we are seeking just now to 
get the principle clearly in mind and we can note the 
setting and difficulties of the method afterwards. 

Examples of Induction by Agreement. One of 
the classic examples in science of the application of this 
method is the discovery by Sir David Brewster that the 
material of mother-of-pearl has nothing to do with the 
brilliant display of color supposed to be characteristic 
of it. By accident, he took an impression of a piece of 
mother-of-pearl in beeswax and found, much to his sur- 
prise, that the colors were reproduced upon its surface. 
His interest being attracted, he carried on the experi- 
ment with other materials such as gum-arabic, balsam, 
etc. In each case, the colors appeared. The inference 
was obvious. The only feature these objects had in com- 
mon was the form secured by impression from the 
mother-of-pearl. 

"When Sir Isaac Newton was investigating the prop- 
erty of physical objects called ' mass,' he had to deter- 
mine that the material of which the body was made did 
not affect this property. In the same way, Galileo proved 
that bodies fall to the ground at a rate irrespective of 
their weight by the simple expedient of dropping bodies 
of different weights from the leaning tower of Pisa. 

Let us suppose that an epidemic of typhoid fever 
has appeared in a city. In order to prevent its further 
spread, the health authorities will wish to locate the 
source of the disease. Past experience will suggest cer- 
tain possible sources, such as the milk supply, the water 



CAUSAL RELATIONS 217 

supply, the food, etc. Examining the milk supply, the 
authorities may find that the various patients secure 
their milk from different dairies. This fact makes the 
milk an improbable source. Turning to the food supply, 
they may find that no one article of food is obtained 
at the same store. The water supply, on the other hand, 
is common. This agreement will suggest to them very 
strongly that the infection was spread by contaminated 
water. ' If, furthermore, they find no other common 
articles of consumption, they will undoubtedly conclude 
that the water supply was at fault. 

The Character of the Method. The Method of 
Agreement is more one of observation than of experi- 
mentation. As a rule, a large number of instances is 
necessary in order to make certain the inclusion of the 
cause among the factors noted. In practice, the method 
is preliminary and does not do much more than elimi- 
nate theoretically possible factors and narrow down the 
field for experimentation. It is an empirical way of 
approach to a problem and stresses observation. It does 
not get us far beneath the surface of things. " Thus 
varying the circumstances so as to bring out a common 
antecedent, though it does not end in exact proof, may 
indicate causal connection though it does not prove what 
the nature of the connection is. Roger Bacon's obser- 
vations indicated that the production of rainbow colors 
was connected with the passage of light through a 
transparent globe or prism. It was reserved for Newton 
to prove by other methods that white light was composed 
of rays, and that those rays were differently refracted 
in passing through the transparent medium." 1 
1 Minto, Logic, Inductive and Deductive, p. 325. 



218 THE ESSENTIALS OF LOGIC 

Difficulties confronting the Method. There are 
two important difficulties confronting this method. 
First comes the inability to determine in any dogmatic 
way what factors are present ; and, added to this, the 
possibility that the effect may be produced by different 
factors on different occasions. Let us examine these 
difficulties somewhat closely. 

It is so easy to ignore factors because they do not 
seem to have any connection with the effect. Hasty 
elimination of factors as the result of prejudice can 
easily lead to false results. Again, analysis is often too 
incomplete to enable the observer to recognize the con- 
stant factor. A very good instance of this oversight of 
the really important factor was the theory, held before 
the part played by micro-organisms in the propagation 
of disease was understood, that night air was the cause 
of malaria. It was noticed that people who caught ma- 
laria were generally exposed to the night air, but the 
fact that they were bitten by mosquitoes was not thought 
important and was therefore disregarded. 

The fact that about the same effect can be produced 
by several causes is expressed by the phrase, ' plurality 
of causes.' Death, for instance, can be caused in many 
ways, and so can headaches and sickness generally. 
The common factor — when I take only a few cases — 
may not be the effective antecedent. My headache may 
be caused one night by smoking a cigar and, another 
night, by drinking too much coffee. We must conclude 
that the method of agreement is preliminary and that 
it is final in very simple cases only. The scientist re- 
gards it as a stepping-stone to experimentation; it 
leads to guesses which can be tested. 



CAUSAL RELATIONS 219 

The Method of Difference. " If an instance in 
which the phenomenon under investigation occurs, and 
an instance in which it does not occur, have every cir- 
cumstance in common save one, that one occurring only 
in the former ; the circumstance in which alone the two 
instances differ is the effect or the cause, or an indis- 
pensable part of the cause, of the phenomenon." A more 
succinct statement of the canon, bringing out its experi- 
mental character, is as follows : " When the addition of 
an agent is followed by the appearance, or its subtrac- 
tion by the disappearance, of a certain event, other 
circumstances remaining the same, that agent is the 
cause of the event." l It should be noted that only one 
factor should be changed. Great technical skill is often 
needed to fulfill this essential condition. The investi- 
gator must have control of his material. 

Examples of the Method. Suppose we have been 
led to ask ourselves why it is that a feather does not 
fall to the ground as fast as does a stone. The idea 
may come to us that the presence of the air is the 
cause. If we can remove this and keep the other fac- 
tors the same, we will be able to test our conjecture. 
The two instances will be as follows : — 

Antecedent conditions Effect 

1st instance : stone and feather dropped in stone falls first 

the air 
2d instance: stone and feather dropped in both fall together 

a vacuum 

This method is used primarily in physics and chem- 
istry, for the material of these sciences lends itself to 
a literal analysis and synthesis under experimental con- 

1 Mellone, An Introductory Text-Book of Logic, p. 274. 



220 THE ESSENTIALS OF LOGIC 

ditions. It is less e^sy to apply it to organisms and to 
social conditions. 

Warnings. When the method can be applied under 
experimental conditions so that only one factor varies, 
the only danger lies in the interpretation of the result. 
The factor may not be the only cause which is able to 
produce the effect. A plant may die when water is 
withheld, but it will also die when heat is removed. A 
positive effect often demands the cooperative presence 
of many conditions, and then the removal of any one 
of these will prevent the occurrence of the effect. An- 
other difficulty lies in the possible presence of counter- 
acting causes. A man who is very healthy may be able 
to resist infection, and so may a man who has had the 
disease and is now immune. So long as there is incom- 
plete analysis of the situation, interpretation of the 
result of an experiment has its dangers. Only as fur- 
ther knowledge is gained, does the only possible inter- 
pretation begin to stand out. 

When experimental conditions cannot be obtained, 
there is great danger that the two instances may 
differ in more than one point. " As an exemplifi- 
cation of this, we may cite an inference that was sup- 
posed to be warranted by the experience of one of our 
larger cities, which had voted to increase materially 
the price of liquor licenses. The police records, for the 
period immediately subsequent to the time when the 
new law went into effect, showed a distinct decrease in 
the amount of crime. By the method of difference we 
should naturally attribute this fact to the high license. 
But it was found that after the election the officials 
who issued the licenses had been much more careful 



CAUSAL RELATIONS 221 

than' before to issue licenses only to applicants of good 
moral character. This fact alone might account for the 
decrease in crime, leaving the higher license without 
effect upon the result." 1 

The Method of Concomitant Variations. 
" Whatever phenomenon varies in any manner, ichen- 
ever another phenomenon varies in some particular 
manner, is either a cause or an effect of that phenom- 
enon, or is connected with it through some fact of 
causation" The development of quantitative methods 
in modern science has made it possible to measure the 
variations of the important antecedents of an effect 
and to note corresponding variations in the effect 
itself. This mode of procedure is especially valuable 
when the conjectured cause cannot be removed com- 
pletely but only decreased and increased. The method 
can be used either as a substitute for the Method of 
Difference or as a reinforcement of it when the interest 
of the experimenter travels to the study of the quanti- 
tative aspects of the causal relation. 

Examples of the Method. The history of science 
is replete with instances of the application of the 
Method of Concomitant Variation. By the experiment 
of Count Kumford, heat was shown to be the effect of 
motion. " In this famous experiment, which disproved 
the material theory of heat, a blunt steel borer 3J 
inches wide was turned by horse power 32 times a 
minute inside a brass cylinder weighing 113 pounds. 
In two and a half hours the water surrounding the 
cylinder and weighing 18| pounds was heated from 
60° F. to the boiling point. Only 4145 grains of 
1 Bode, An Outline of Logic, p. 139. 



222 THE ESSENTIALS OF LOGIC 

the metal were abraded. Rumford correctly concluded 
that this large amount of heat, which appeared to be 
inexhaustible, could not have been derived from the 
abraded metal, which at the same time had not lost 
any of its capacity for heat." x The First Law of 
Motion, Boyle's Law, the theory of the thermometer, 
the connection of air with the propagation of sound 
are all dependent, in whole or in part, upon the use of 
this method. 

Warning. This method stresses the ratio between 
the change in the causal factor and the change in the 
effect. It has been found, however, that there is such 
a thing as discontinuous variation. Metals do not 
continue to expand at the same rate as the temperature 
increases, nor do they contract at the same rate as the 
temperature is lowered. Another point should be 
noted. It often happens that both of the quantities 
measured are co-effects of a third factor. Hence, where 
possible, the Method of Concomitant Variations should 
be supplemented by the Method of Difference. 

The Joint Method of Agreement and Differ- 
ence. " If two or more instances in which the phe- 
nomenon occurs have only one circumstance in com- 
mon, while two or more instances in which it does not 
occur have nothing in common save the absence of that 
circumstance, the circumstance in which alone the two 
sets of instances differ is the effect, or the cause, or an 
indispensable part of the cause, of the phenomenon" 
The Joint Method is a combination of the Method of 
Agreement and the Method of Difference, and is espe- 
cially applicable when experimental conditions are not 

1 Carhart, University Physics, pt. n, p. 4. 



CAUSAL RELATIONS 223 

obtainable. It is a method of group comparisons. The 
investigator collects cases in which the desired effect 
is present and compares the instances to see in what 
they agree ; he then collects other cases in which the 
effect is absent and compares these instances to see in 
what they agree. Finally, he examines the two groups 
to see wherein they differ. In this way, he approaches 
as nearly to the Method of Difference as can be done 
without experimentation. Without some control of the 
factors, the conclusion can be regarded only as tenta- 
tive. 

Examples. " The following instance illustrates the 
use of the Joint Method of Agreement and Difference : 
A large number of cases of typhoid fever occurred at 
about the same time in a college community. It hap- 
pened that all those who developed the disease ate at a 
certain few fraternity and boarding-house tables. The 
water supply was first investigated. It was found that 
all these places used water from the same source. But 
it was also true that the other houses were supplied 
from the same source, so this possible cause was elimi- 
nated. The fresh vegetables were supplied from vari- 
ous sources ; some of the places in which the disease 
was developed used one source, others a different one ; 
moreover, the places in which the disease was not de- 
veloped were supplied from the same variety of sources. 
The other food supplies came from various places and 
the Method of Agreement could not be applied so far 
as they were concerned, with one exception ; it appeared 
that the milk supply was the same for all the places in 
which the fever was developed, whereas none of the 
places which escaped used milk from that source. The 



224 THE ESSENTIALS OF LOGIC 

inference was that the milk contained the cause of the 
disease. Further, it was found that when milk from 
this source was no longer used, no new cases of the dis- 
ease appeared." l Another good example is to be found 
in the work of Darwin upon the cross-fertilization of 
flowers. In this investigation, Darwin placed a net 
about one hundred flower heads to protect them from 
bees. At the same time he exposed another hundred 
flowers to the bees. Here we have the two groups be- 
tween which comparison is to be made. He obtained 
the following results : The protected flowers failed to 
yield a single seed, while the others produced 68 grains' 
weight of seed, which he estimated as numbering 2720 
seeds. 

These examples show that the Joint Method is really 
the complete application of the two principles of Agree- 
ment and Difference, and that any exhaustive investi- 
gation is bound to take this form. Another point stands 
out clearly. In any actual study the mind is always 
making conjectures and testing them by these methods. 
The scientist is not a merely passive tabulator. He 
knows that the cause must be present when the effect is, 
and that it must be absent when the effect is absent. 
Hence, he is on the constant lookout for factors which 
may fulfill these conditions. 

The Method of Residues. " Subduct from any 
phenomenon such part as is known by previous indue- 
tions to be the effect of certain antecedents, and the res- 
idue of the phenomenon is the effect of the remaining 
antecedents." This method can be employed only when 
there is nearly complete information in regard to the 
1 Jones, Logic, Inductive and Deductive, pp. 98-99. 



CAUSAL RELATIONS 225 

field under investigation. By means of this knowledge, 
we are able to eliminate causal couples until we are left 
with the few factors remaining for which causal rela- 
tions have not been determined. In this way, past 
knowledge enables the investigator to narrow the field. 
After this is accomplished, he can observe more closely 
and often experiment. Like the Method of Agreement, 
the Method of Residues is usually a preliminary pro- 
cess which needs supplementation. 

Examples. The Method of Residues comes out 
most clearly where quantitative methods are being em- 
ployed. For astronomy, the classic example is the dis- 
covery of the planet Neptune. Certain perturbations in 
the movement of Uranus could not be accounted for 
by known gravitational forces. The natural inference 
was that some unknown planet was at work producing 
this added increment, the residual effect. Adams in 
England and Leverrier in France made this hypothesis 
independently of each other and calculated the prob- 
able place of the new planet. Following the directions 
of the latter, Professor Galle, of Berlin, found the new 
planet in almost exactly the place indicated. Another 
instance of discovery due to residual effects is that of 
the rarer elements in the atmosphere such as argon and 
helium. "In chemical analysis this method is con- 
stantly employed to determine the proportional weight 
of substances which combine together. Thus the com- 
position of water is ascertained by taking a known 
weight of oxide of copper, passing hydrogen over it in 
a heated tube, and condensing the water produced in 
a tube containing sulphuric acid. If we subtract the 
original weight of the condensing tube from its final 



226 THE ESSENTIALS OF LOGIC 

weight we learn how much water is produced; the 
quantity of oxygen in it is found by subtracting the 
final weight of the oxide of copper from its original 
weight. If we then subtract the weight of the oxygen 
from that of the water we learn the weight of the hy- 
drogen, which we have combined with the oxygen." 1 

This method is primarily one of quantitative analy- 
sis. It concerns itself with residual phenomena, with 
exceptions. Speaking of his father, Francis Darwin 
says : " There was one quality of mind which seemed to 
be of special and extreme advantage in leading him to 
make discoveries. It was the power of never letting 
exceptions pass unnoticed." Such a habit of mind is 
assuredly worth cultivation. 

Remarks on Mill's Methods. There is pretty 
general agreement now among logicians that Mill's 
Methods can be employed only within a larger induc- 
tive setting. They are not rules which can be applied 
mechanically to new and complex fields. The mind 
must be active in conjecture, interpretation and analy- 
sis. In the first part of his Logic, Mill is far more Bacon- 
ian than he is in the latter part. The following quota- 
tion gives all the correction that is needed and reveals 
how the Methods are taken up into the concrete process 
of investigation : " The process of tracing regularity in 
any complicated, and at first sight confused set of ap- 
pearances, is necessarily tentative : we begin by making 
any supposition, even a false one, to see what conse- 
quences will follow from it; and by observing how 
these differ from the real phenomena, we learn what 
corrections to make in our assumption." Increasing 

1 Jevons, Lessons in Logic, p. 254. 



CAUSAL RELATIONS 227 

analysis, working hypotheses, gradual elimination of 
irrelevant factors, and final decision as to the essential 
connections are the steps in induction. 

REFERENCES 

Creighton, An Introductory Logic, chaps, xvi and xvn. 

Gibson, The Problems of Logic, chap. xiii. 

Jones, Logic, Inductive and Deductive, chap. vi. 

Mill, Logic, bk. in, chaps, vin and ix. 

Minto, Logic, Inductive and Deductive, bk. n, chaps, in, iv, and v. 



CHAPTER XX 

STATISTICS 

In many fields of investigation it is impossible to 
apply the traditional methods. The problem is of such 
a character and covers such a wide territory that indi- 
vidual observation cannot furnish the factual material. 
Furthermore, experimental methods cannot be applied. 
What is needed is a very broad survey of the facts and 
a clear tabulation of the results obtained. Out of this 
necessity has arisen statistical science. "It would be a 
man of exceptional mnemonic power who could, after 
listening to the reading of two lists of one hundred 
items each stating the names and wealth of the respec- 
tive inhabitants of two villages, give any intelligent 
opinion as to the comparative riches of the two communi- 
ties. If this is true for such small groups as this, it evi- 
dently would be utterly impossible to make comparisons 
of the wealth of great nations without some manner of 
reducing the mass of separate facts to a simple whole. 
The same would, of course, be true in the case of any 
other phenomena involving large numbers. What could 
one understand of the amount of lumber contained in a 
forest from a description of the separate trees ? How 
could one compare the climates of different localities by 
a study of their daily weather records ? It is for the 
purpose of simplifying these unwieldy masses of facts 
that statistical science is useful. It reduces them to 
numerical totals or averages which may be abstractly 



STATISTICS 229 

handled like any other mere numbers. It draws pictures 
and diagrams to illustrate general tendencies and, thus, 
in many ways adapts these groups of ideas to the capac- 
ity of our intellects." 1 

If the student will recall the discussion of " Classi- 
fication," he will remember that it was regarded as a 
process which enables us to handle the complex world 
of individual things in which we live. Could we not 
treat things as kinds and know what to expect from 
them, we should be unable to adapt ourselves to our 
environment by using our past experience. Now, statis- 
tics is a way of dealing with particulars which can be 
counted and which are so numerous that we need to 
achieve some bird's-eye view of them before we can 
begin to interpret them. It is a way of collecting and 
organizing data which are important in masses rather 
than individually. " The proper function of statistics," 
writes Bowley, "is to enlarge individual experience." 
Originally the workers in statistics concerned them- 
selves almost entirely with facts respecting the condition 
of the people in a state, but now data in biology and 
astronomy are also investigated by statistical methods. 

We have frequently pointed out that science always 
involves analysis. Mental work must be done upon the 
facts before they yield a meaning and can be applied 
to the solution of a problem. This element stands out 
very clearly in the following definition of statistics : 
" The science of statistics is the method of judging col- 
lective natural or social phenomena from the results 
obtained by the analysis of an enumeration or collec- 
tion of estimates." 2 

1 King, Elements of Statistical Method, p. 24. 2 Ibid., p. 23. 



230 THE ESSENTIALS OF LOGIC 

The stages in a statistical investigation are roughly 
as follows : (1) The setting of the problem ; (2) the 
collection of the material ; (3) its tabulation ; (4) the 
summary; (5) a critical examination of the results. 
Let us look at these stages somewhat closely. 

" Special importance, it seems, must be attached to 
the question of what are the objects of any particular 
statistical record. It is not enough to observe the facts 
at random. Most of the records of statistics, although 
not all of them, are deliberately arranged to be kept by 
a community for the purpose of the information of the 
whole community. . . . The object, then, of any par- 
ticular statistical record is the first thing about it to be 
studied, and both the Government in making the rec- 
ords and the students who come to use them afterwards 
should have the most distinct ideas upon this point." l 
This point is stressed by all statisticians. " The first 
thing upon which the statistical investigator, when be- 
ginning his work, must decide is the exact nature of 
the problem which he desires to solve. Even a slight 
change in its scope or form may require an entirely or 
partially different method of procedure. If, for illustra- 
tion, a person wishes to begin a study of comparative 
wages in order to demonstrate some general theory or 
proposition, he must first decide as to whether the re- 
quirements of his problem demand a knowledge of 
money wages or real wages. Next, he must be sure as to 
whether he needs to know the wages paid for a definite 
amount of effort, for making a certain product, or for 
working a certain length of time, or whether the in- 
quiry relates to the income of the working man him- 

1 Sir Robert Giffen, Statistics, pp. 4-5. 



STATISTICS 231 

self per year or to the total income of the man and 
his family for the same period. Each of these problems 
is a distinct one and would require entirely different 
modes of determination." 1 

Definition of the problem also involves definition of 
the unit. What shall we mean by 'unemployment' ? by 
4 person ' ? by * a farm ' ? by 4 sickness ' ? Just as classi- 
fication and its principles are important for statistical 
investigation, so is definition. Thus a recent work on 
Unemployment gives a chapter to the "Meaning and 
Measurement of Unemployment " and devotes much of 
its space to the working-out of a definition. " Are we, 
for example, to include among the unemployed those 
who are idle because they do not want to work ? Are 
we to include sick persons, or workmen out on strike, 
or the various classes of individual who are, for one 
reason or another, 'unemployable'?" Just as an idea 
must not be allowed to change its meaning in the course 
of an argument, so the unit must not be altered in the 
course of an investigation. The prerequisites of clear 
thinking are essentially the same for argument of a 
deductive character and for investigation. 

Before the collection of the material is begun, the 
problem must be studied in all its details. " Problems, 
factors, units, questions, schedules, enumerators, tabu- 
lation, methods of work, time, expense, etc., are among 
the items that must be carefully gone over in minute 
detail." The methods of collection must be determined 
by experience with due regard to the characteristics of 
the particular problem. The field must be defined and 
must be as wide as possible. If questions are used, these 

1 King, Elements of Statistical Method, p. 39. 



232 THE ESSENTIALS OF LOGIC 

must be comparatively few in number, must be simple 
enough to be readily understood, and must not arouse 
prejudices. As in all the other divisions of science, per- 
sonal judgment cannot be eliminated. Investigation is 
not a mechanical process. 

" With the collection of statistical data, only the first 
step has been taken. The statistics in that condition are 
only raw material showing nothing. They are not an 
instrument of investigation any more than a kiln of 
bricks is a monument of architecture. They need to be 
arranged, classified, tabulated, and brought into con- 
nection with other statistics by the statistician. Then 
only do they become an instrument of investigation, 
just as a tool is nothing more than a mass of wood or 
metal, except in the hands of a skilled workman." * The 
figures must be grouped in tables under appropriate 
headings in such a way as to bring out the desired per- 
centages and correlations. " The power to analyze a 
table, interpret the results correctly, and state the con- 
clusions lucidly and succinctly is one of the character- 
istics indispensable in a good statistician." 

The Law of Statistical Regularity. It has been 
discovered that a moderately large number of items 
taken at random from a very large group, are almost 
sure, on the average, to have the characteristics of the 
larger group. " Thus, if two persons, blindfolded, were 
to pick here and there three hundred walnuts each from 
a bin containing a million nuts, the average weight of 
the nuts picked out by each person would be almost 
identical even though the nuts varied considerably in 
size." Corresponding to this law is its corollary, the 

1 Mayo-Smith, Statistics and Sociology, p. 18. 



STATISTICS 233 

law of inertia of large numbers. Logicians have been 
accustomed to speak of this law as the constancy of 
averages. " If we take a succession of periods, and di- 
vide the total number of any kind of event by the num- 
ber of periods, we get what is called the average for 
that period: and it observed that such averages are 
maintained from period to period. Over a series of 
years there is a fixed proportion between good harvests 
and bad, between wet days and dry : every year nearly 
the same number of suicides takes place, the same num- 
ber of crimes, of accidents to life and limb, even of sui- 
cides, crimes, or injuries by particular means: every 
year in a town nearly the same number of children 
stray from their parents and are restored by the police : 
every year nearly the same number of persons post 
letters without putting an address on them." 2 

Dangers in the Use of Statistics. Great care 
must be taken in the use of statistics. It has been said 
that " you can prove anything by statistics." And this 
skepticism reflects the constant misuse of figures. Every 
stage in the development of tables is liable to its pecul- 
iar errors which resemble those which face all inves- 
tigation. Prejudice, inaccuracy, faulty observation, 
mistakes in copying, wrong interpretation, all exist as 
possible sources of falsehood. Another cause of error is 
the lack of recognition given to the difference between 
quantity and quality. " In sociological science the im- 
portance of differences of quality is enormous, and the 
effect of these differences on the conclusions to be 
drawn from figures is sometimes neglected, or insuffi- 
ciently recognized, even by men of unquestionable 
1 Minto, Logic, Inductive and Deductive, p. 351. 



234 THE ESSENTIALS OF LOGIC 

ability and good faith. The majority of politicians, so- 
cial ' reformers ' and amateur handlers of statistics gen- 
erally are in the habit of drawing the conclusions that 
seem good to them from such figures as they may ob- 
tain, merely by treating as homogeneous quantities 
which are heterogeneous, and as comparable quantities 
which are not comparable. Even to the conscientious 
and intelligent inquirer the difficulty of avoiding mis- 
takes in using statistics prepared by other persons is 
very great. There are usually 'pitfalls' even in the 
simplest statistical statement, the position and nature 
of which are known only to the persons who have actu- 
ally handled what may be called the ' raw material ' of 
the statistics in question; and in regard to complex 
statistical statements the ' outsider ' cannot be too care- 
ful to ascertain from those who compiled them as far 
as possible what are the points requiring elucidation." 1 
So frequent a use is made of statistics now that the 
logician feels it a part of his duty to stress these 
warnings. The following example may serve to indicate 
how easily fallacy may creep in : " An example of such 
a fallacy, due to the use of erroneous factors, was fur- 
nished by a newspaper in a discussion of the American 
navy during the Spanish- American War. It was stated 
that the death-rate in the navy during the war period 
was only nine per thousand, while in the city of New 
York for the same period the death-rate was sixteen 
per thousand. The conclusion was drawn that it was 
safer to be a sailor in our navy in war-time than to live 
in New York City. A little reflection, however, will 
convince one that such a conclusion is not warranted 

1 Encyclopaedia Britannica, art. " Statistics." 



STATISTICS 235 

by the figures given. In obtaining this ratio, the total 
number of deaths was taken as the numerator in each 
case and the denominators were respectively the total 
number of persons living in New York City and the 
total number of sailors in the navy. But, as a matter 
of fact, these numbers were wholly incomparable. It is 
a well-known fact that the death-rate is very high 
among young children and among old people. But the 
personnel of the navy is composed almost wholly of 
young men in the prime of strength and vigor. Not 
only this, but each must pass a strict examination to 
show that he is healthy and robust. Thus, the weak 
and diseased are eliminated. Evidently, the facts would 
require that the death-rate in the navy be compared 
with the death-rate of a similar picked body of men in 
New York City before any legitimate conclusions could 
be drawn regarding the comparative chances of death 
in the two places." * 

The Value of Statistics. There are three main 
ends subserved by statistics : Its employment contrib- 
utes to a descriptive survey of a field which cannot be 
otherwise grasped. Figures are then merely a method 
of expressing facts, as the amount of wheat produced, 
the quantity of exports, the amount of the national 
wealth. Such information is often of the greatest sig- 
nificance. We may wish to compare one country with 
another, or the same country at different times. Very 
frequently the data obtained can be used to test a theory 
which has been worked out more or less deductively. 
Wherever there is induction, there must be appeal to 
relevant fact ; and in many fields, statistics is the only 

1 King", Elements of Statistics, p. 40. 



236 THE ESSENTIALS OF LOGIC 

means of securing such facts. In the second place, the 
discovery of averages which are fairly constant enables 
man to predict the general run of cases in the future. 
As we shall see in the next chapter, the theory and 
practice of life insurance are founded upon the exist- 
ence of such averages which are being continually de- 
veloped and rendered more accurate. In the third 
place, tables of statistics often reveal correlations which 
would not otherwise have been discovered because of 
the complexity of the material and our inability to ana- 
lyze it into distinct strands of causal uniformities. 
When data are properly arranged, the field is condensed 
and simplified and it is possible to note relations which 
would have remained hidden. The use of graphs is 
often an aid because they make a direct appeal to the 
eye. An example of a correlation which suggests the 
presence of causal relations is the fluctuation of the num- 
ber of births in a country correspondent with the food 
prices of the previous year. Let us consider this third 
function of statistics a little more fully. 

The principle underlying the deduction of causal re- 
lations from correlations is the assumption that if the 
events are unconnected, their frequencies should not 
fluctuate together nor coincide beyond a certain amount. 
Bain formulated the following rule : " Consider the 
positive frequency of the phenomena themselves, and 
how great frequency of coincidence must follow from 
that, supposing there is neither connection nor repug- 
nance. If there be greater frequency, there is connec- 
tion ; if less, repugnance." Repugnance is usually spoken 
of in statistics as negative correlation. An example 
would be the relation between vaccination and small- 



STATISTICS 237 

pox. In delicate cases, it is very difficult to estimate 
the degree of coincidence between non-causal events. 
How often, for instance, must dreams and their apparent 
fulfillment coincide to pass beyond mere coincidence ? 

Variation in averages is a fruitful source for the dis- 
covery of causal relations. If we assume that the con- 
stancy of the averages is due to the maintenance of the 
relative proportions of the same factors in the field 
under investigation, then any change in the average 
must be due to an alteration in this proportion or to 
the entrance of a new factor. A study of the geo- 
graphical distribution of suicide is a good instance of 
the suggestive character of comparative statistics. We 
immediately ask ourselves why one country leads, what 
can be the peculiar conditions which cause more people 
to commit suicide there. It will be noted that such 
comparison involves a near approach to the method of 
differences. But experiment is impossible. When an 
average begins to change, the investigator seeks the pres- 
ence of some new cause or the increase of some cause 
already operative. " The number of homicides in the 
United States in 1894 far exceeded the annual num- 
ber observed for the years preceding. This discrepancy 
is easily accounted for by the fact that the natural 
number was swollen by the deaths caused by the strik- 
ers and rioters in the month of July of that year. So 
also a marked departure from the annual death-rate of 
such a city as New York is at once an urgent sugges- 
tion to the Board of Health to start investigations that 
will unearth the hidden cause that one is constrained 
to believe must be present. Such causes as defective 
drains, prevalence of epidemics, etc., are again and 



238 THE ESSENTIALS OF LOGIC 

again found to accompany an increase of the average 
death-rate." * The principle involved is essentially that 
of concomitant variation. 

REFERENCES 

King, Elements of Statistical Method, chaps, I, n, and in. 

Bowley, Elements of Statistics, passim. 

G iff en, Statistics, chap. i. 

Creighton, An Introductory Logic, chap. xv. 

Elderton, Primer of Statistics. 

Hibben, Logic, Deductive and Inductive, chap. xv. 

Mayo-Smith, Statistics and Sociology, chaps. I, n, and ill. 

1 Hibben, Logic, Deductive and Inductive, p. 344. 



CHAPTER XXI 

PROBABILITY 

Abstract Laws versus Concrete Events. While 
the physical sciences are chiefly interested in the dis- 
covery of universally valid causal laws and in the 
construction of illuminating general principles and 
theories, problems of another sort come to the front in 
practical life, the applied sciences, and those fields of 
research in which experimental control is impossible. 
Where experiment is possible, factors can be eliminated 
as irrelevant or confusing, and the remaining elements 
can then be analyzed into couples uniformly connected. 
But where such experimental control and simplification 
is out of the question, causes counteract one another in 
the most complex ways or else combine to produce 
effects which are not deducible from any one of them. 
In other words, such causal uniformities as we discover 
by experiment are blurred when they enter this whirli- 
gig of a world, and it is with the greatest uncertainty 
that we predict the course of events. 

In science, the investigator usually passes from effect 
to cause; in everyday life, the problem is to pass from 
the play of events to the probable result. What it is 
now desired to ascertain is what will probably happen 
in the tangled skein of events which cannot be com- 
pletely analyzed beforehand. Will the country be 
prosperous a year from now or plunged in a panic? 
Will this bank be solvent or will it fail? Will the 



240 THE ESSENTIALS OF LOGIC 

crops be good this year? Such questions make us 
realize the complexity of things and our inability to 
deduce events from the few uniformities we have as 
yet discovered. Most laws have their exceptions be- 
cause the essential factors are masked by the interplay 
of their fellows. 

"Where Certainty is possible. Certainty as to the 
future is possible only when all the factors whose opera- 
tions will produce it are known. Moisture causes 
plants to grow when it is combined in the proper pro- 
portion with heat and sunshine and good soil. It is 
evident that quantities are important if we are to pre- 
dict. Thus, we must have knowledge of the essential 
conditions, qualitative and quantitative, of an event 
and have assurance of their presence before we have 
the logical right to predict an event with certainty. In 
a carefully conducted experiment in chemistry where 
quantities and qualities are both under control, expec- 
tation is based on exact knowledge, and all that we need 
to assume is the general principle of the Uniformity of 
Nature. Again, prediction is possible in astronomy 
where the forces at work are relatively few in number 
and measurable. In this realm of giant masses and gravi- 
tational forces acting according to well-known laws, it 
is possible to foretell the relative positions of bodies 
and so arrange in tables, centuries ahead or behind the 
present, those eclipses and juxtapositions which are of 
human interest. But when the antecedents cannot be 
analyzed in this fashion and are known to be more 
fluctuating in their permutations and combinations, 
prediction loses certainty and drops to probability. 

The Meaning of Probability. Probability at- 



PROBABILITY 241 

taclies to particular facts and to generalizations. We 
use the term when we feel that the balance of evidence 
is in favor of a principle or an individual fact even 
though it has not been raised above reasonable doubt. 
So far as principles are concerned, their probability re- 
flects the degree to which they are supported by the 
collected evidence. It may be that all the evidence 
thus far attained is favorable but that we do not re- 
gard it as extensive enough ; or it may be that the evi- 
dence is conflicting. When we are concerned with the 
probability of the occurrence of an event, on the other 
hand, we are attempting to make an estimate of our 
admittedly insufficient knowledge to determine whether 
it is in favor of, or against, this particular occurrence. 
We temper the degree of our expectation in accordance 
with such relevant knowledge as we can gather. In 
contrast with certainty, we may say that probability is 
the degree of expectation which is judged to be war- 
ranted by the facts. We say that an event is probable, 
or quite probable, or very probable, or extremely 
probable. 

Probability and Chance. Probability must not 
be confused with objective chance. The principle of the 
Uniformity of Nature is essentially the denial of any- 
thing like real chance in the world. But nature is so 
complex that we are not able to note and analyze all 
the conditions of the majority of events. Causal fac- 
tors reinforce and counteract one another in unforeseen 
ways, and the actual result can be learned only from 
experience. That I turned up an ace of spades the last 
time I cut for the deal was, so far as my knowledge 
went, a case of chance. In short, chance is a term ex- 



242 THE ESSENTIALS OF LOGIC 

pressive of my ignorance of what is taking place. 
"There is no doubt in lightning,' ' writes Jevons, " as 
to the point it shall strike ; in the greatest storm there 
is nothing capricious; not a grain of sand lies upon 
the beach but infinite knowledge would account for its 
lying there ; and the course of every falling leaf is 
guided by the same principles of mechanics as rule 
the motions of the heavenly bodies." 1 

Three Kinds of Estimations. Eoughly speaking, 
we may distinguish three kinds of probability-estima- 
tions. The first is empirical and largely qualitative; 
the second deals with averages and is closely connected 
with the development of statistics ; the third is of a de- 
ductive, mathematical type. What logic is interested 
in is the nature of the induction and the dangers 
run. 

1/ Empirical, or Non-Quantitative, Probability. 
As regards most events, we do not keep any exact record 
of how things have happened in the past, but trust 
to a general impression, to a sort of cumulative esti- 
mation expressive of past experience. This judgment 
is then related to the particular circumstances of the 
case in hand and a feeling of probability arises in con- 
sciousness. Suppose that you hear that a person whose 
name is not given has met with an accident in the city 
of Washington. The idea may come to you that it may 
be your brother who lives there ; but the idea is sure 
to be dismissed unless other information points in the 
same direction. Suppose that the accident happens in 
a government building where he works, and that the 
description of the individual tallies somewhat with his 

1 Principles of Science, vol. I, p. 225. 



PROBABILITY 243 

appearance, your passing idea begins to be entertained 
more seriously and you await some letter or telegram. 
If it does not come within a day or so, you dismiss the 
suggestion. You know that there are many govern- 
ment employees and that rough descriptions apply to 
large numbers of individuals equally well. 

Probabilities based on Averages. A frequently 
employed method of calculating probabilities is the 
study of averages for classes. Sometimes such a study 
is non-statistical, but it readily passes into the stage of 
statistics. An individual may calculate that he has many 
more years to live because he is healthy and fairly 
young and is working in a profession where the risks 
are small. " This type of reasoning is duplicated in 
many other instances. When we mail a letter, we 
count pretty confidently upon its safe arrival. From 
time to time, letters get lost, through carelessness, in 
railroad wrecks, or as a result of other causes, but the 
number of those is so small a proportion of the total 
number that we treat it as practically a negligible 
quantity. For the same reason we leave out of account 
the possibility that at some time we shall be struck by 
lightning, or, when we make a journey, that our train 
will be wrecked, or that our home will be destroyed by 
an earthquake, or that a stranger o£ whom we make 
inquiries as to directions will be insolent or show an- 
noyance." 1 

The best familiar example of the calculation of prob- 
abilities for a class is to be found in the field of life in- 
surance. Tables are worked out for the various trades 
and professions and for individuals of different ages. 

1 Bode, An Outline of Logic, p. 150. 



244 THE ESSENTIALS OF LOGIC 

Any applicant is classified and his probable length of 
life estimated by reference to the group in which he is 
classified. A danger of fallacy lurks in this method 
when its meaning is misunderstood. It must be borne 
in mind that such probability only applies to the class 
and not directly to the individual. We are not able to 
predict which individuals will die, but only that about 
so many out of every thousand of a certain age will die. 
It is upon the constancy of these averages that the com- 
pany calculates the necessary premium. 

Estimates of probability are made more accurate by 
deepening the classifications made. The greater the 
number of essential characteristics that are included, 
the smaller and more homogeneous the class.t-Thus, 
teachers and ministers are known to have a far longer 
average of life than miners and textile workers. Statis- 
tics have shown that the average length of life of the 
rich is greater than that of the poor. It has been esti- 
mated that in England the average duration of life 
among the wealthy classes is from fifty-five to fifty-six 
years, while in the working classes it falls to twenty- 
eight years, or even lower. 

A word of warning may, perhaps, be advisable at 
this point. Probability of this objective sort is based 
on the use of statistics. Now the growth of statistics 
has shown a constancy in the number of crimes com- 
mitted in a certain country in the course of a year, in 
the number of suicides, in the number of fires, etc. 
In the preceding chapter, we spoke of this regularity as 
the 4 law of inertia of large numbers.' The meaning of 
this law has been much misunderstood, many fearing 
that it implied a kind of mechanical necessity at work 



PROBABILITY U5 

in society corresponding to the 'reign of law ' in nature. 
It is well to bear in mind that such expressions are 
metaphorical and that we must penetrate behind them 
to the exact facts of the case. Laws are human formu- 
lations and do not reign in the physical world by divine 
right or otherwise. In the same way, statistical constan- 
cies are only formulations of data and do not imply any 
fate lying back of, and controlling, society. The follow- 
ing passage from Quetelet, the famous Belgian statis- 
tician, is worth quoting in this connection : " Amongst 
the facts disclosed in my book, the one which has given 
rise to most alarm is the constancy of crime from year 
to year. By a comparison of numbers, I believed I had 
data for inferring, as a natural consequence, that in a 
given country, under the same conditions and influ- 
ences, we might expect a repetition of the same facts, 
a reproduction of the same crimes and the same con- 
demnations. But how was this received ? A crowd of 
timid people raised the cry of fatalism ! Now, what do 
the facts teach us ? This, simply, — that in any given 
state, subject to the influence of the same causes, the 
effects will not differ appreciably ; they will oscillate 
more or less about some mean. Now, mark what I have 
said: subject to the influence of the same causes; so 
that, therefore, if those causes change, the effects will 
be likewise modified. But, since the laws and principles 
of religion and morality are the source of the influences 
in question, I cherish not only the hope, but — what 
you perhaps do not — the deepest conviction even, that 
society can be reformed and ameliorated." The clear- 
sighted student will realize that we are here skirting 
some of the most interesting problems of philosophy. 



246 THE ESSENTIALS OF LOGIC 

What it is important and easy to realize is that con- 
stancy in averages does not involve fatalism. 
^^The Mathematical Treatment of Probability. 
We can divide the mathematical treatment of probabil- 
ity into two parts, the conditions for the application of 
a calculus of probability and the rules for estimating 
probability. 

The first condition for the application of a calculus 
of probability to events is the possession of knowledge 
sufficient to assure us that some one or other of a defi- 
nite number of ways of happening are possible, but not 
sufficient to inform us in which particular way the event 
will occur. There must be this peculiar mixture of 
knowledge and ignorance. " For example, if a penny is 
tossed it will fall with either head or tail uppermost. 
Now, which will be uppermost in any particular throw 
will be exactly determined by such conditions as the 
position of the coin at starting, how it is grasped in the 
fingers, the force and direction of the twist, etc. But 
what special form these conditions will take we are to- 
tally ignorant." 1 The second condition is that the same 
general set of conditions and antecedents must be pres- 
ent and operative during the whole course of the events 
for which a calculation is being made. For instance, to 
substitute another coin with a curve on one of its sur- 
faces for the original one would make a calculation im- 
possible. Both of these conditions are secured in games 
of chance. Since it is not the function of the logician 
to enter into the mathematics of probability in detail 
but only into the logical theory at its foundation, we 
shall consider only the simplest cases. 

1 Welton, Manual of Logic, vol. 11, p. 167. 



PROBABILITY 247 

The probability of a single event is expressed by a 
fraction whose numerator is the number of favorable 
alternatives, and denominator the total number of al- 
ternatives. Since a coin has only two sides, the proba- 
bility of getting heads in any one trial is J. We say 
that the chances for heads and tails are equal and that 
the probability of each is i. In the case of dice, the 
number of sides is greater and, accordingly, the prob- 
ability for any one side is less. The denominator is 6 
while the numerator is 1 for any one side. This is ex- 
pressed in mathematical form by saying that the prob- 
ability for each side is J. The method of reasoning in the 
case of playing cards is essentially the same. The total 
number of possibilities is 52 and the chance for any one 
card is •£%. The chance of getting an ace would be -^ . 

There are two rules with compound events according 
as such events are (1) independent or (2) dependent 
on one another. 

The probability of obtaining any combination of in- 
dependent events is the product of the probabilities of 
the several events. Let us take the throwing of dice as 
an example. " If one die is thrown the probability 
that it will fall with the side bearing six pips upper- 
most is ^, as the die has six sides, and the probability 
of being uppermost is equal for them all. If a second 
die is thrown the probability that in that throw six will 
be uppermost is also 1 ; consequently the probability 
that six will be thrown in each of two throws is i X ^ = -§§ . 
In this case, it is obviously immaterial whether two dice 
are thrown simultaneously or whether the same die is 
thrown successively." 1 Obviously the number of pos- 
1 Welton, Manual of Logic, p. 174. 



248 THE ESSENTIALS OF LOGIC 

sibilities is 36 and only one of these is the combination 
desired. 

If two events are mutually exclusive, the probability 
of getting one or the other is the sum of their inde- 
pendent probabilities. Thus, in throwing dice, the 
probability of getting a six or a five is | -f- J, or J. The 
principle is the same as for simple events. 

We come now to compound events in which the 
occurrence of the first affects the probability of the 
occurrence of the others. In such cases the probability 
of the compound event is the product of the probability 
of the first with the probability of the second as af- 
fected by the first. "For example, what is the proba- 
bility of drawing two white balls in succession, without 
replacing the first drawn, from an urn containing two 
white balls and one black one? If a black is drawn 
first, the estimate is rendered impossible. The proba- 
bility of drawing a white first is |. If it is drawn, the 
constitution of the urn for the second draw is modified 
by the first draw. There are now only two balls, one 
white and one black, in the urn ; and the probability of 
drawing the white is 1." Therefore, the probability of 
drawing two whites is § X J = -J. 

Mistakes in interpreting Probabilities. Mis- 
takes are often made in the interpretation of probabili- 
ties. Probabilities based on averages, as in life insur- 
ance, do not give us any information in regard to any 
particular individual. " Statistics, from the very nature 
of the subject, cannot and never will be able to take 
into account individual cases." 1 When we come to de- 
ductive, or mathematical, probability, other warnings 
1 King-, Elements of Statistics, p. 35. 



PROBABILITY 249 

must be issued, especially for the non-mathematician. 
He must bear the above rules in mind and remember, 
for instance, that the throws " in which we get a six 
with either of two dice are not so common as the throws 
in which we get either a six or an ace with one die. 
We turn up as many sixes with the two dice as we turn 
up sixes and aces with one ; but since the two sixes are 
on different dice and are therefore not incompatible, 
they come together in one throw out of thirty-six, and 
we do not turn them up in so many separate throws." l 
Another point is of interest. The past run of throws 
can offer no basis for an inference as to the character 
of the next throw. " To expect that, because a coin has 
come up heads several times in succession, it is there- 
fore more likely to come up tails the next time, is 
wholly to misunderstand the meaning of probability. 
Indeed, a preponderance of heads in the past throws 
would suggest that the coin was not true, that there was 
a hidden cause favoring heads, and that as a matter of 
fact the probability of heads was greater than one 
half." 2 We see, then, that the calculus of probability 
is only a guide which we take when we cannot secure 
definite information about particular cases. Moreover, 
it is only when certain conditions are fulfilled that the 
probability in favor of a certain occurrence can be esti- 
mated with any large degree of mathematical accuracy. 

1 Aikins, The Principles of Logic, p. 340. 

2 Jones, Logic Inductive and Deductive, p. 223. 



250 THE ESSENTIALS OF LOGIC 



REFERENCES 

Aikins, The Principles of Logic, chap. xxxn. 
Bode, An Outline of Logic, chap. xi. 
Coffey, The Science of Logic, vol. n, p. v, chap. II. 
Jones, Logic, Inductive and Deductive, pt. n, chap. in. 
Welton, Manual of Logic, bk. v, chap. vi. 



CHAPTER XXII 

AVERAGES AND GRAPHS 

The Uses of Averages. In the two preceding chap- 
ters we have had frequent occasion to speak of aver- 
ages. Statistics does not concern itself with the individual 
case, but with the average for a group or collection. 
Thus, we are presented with the average income per 
capita, the average number of rooms in the houses oc- 
cupied by working people, the typical expenditure of a 
family for food, etc. Insurance, industrial, and health 
statistics all take this form. It behooves us, therefore, 
to have some knowledge of the methods used in obtain- 
ing such averages and the ways in which they are best 
presented to the mind. 

The following uses summarize very well the view of 
the modern investigator : — 

"Averages are used: 1. To give a concise picture 
of a large group. We could not grasp the idea well 
if given the height of every tree in a forest, but the 
average height is something definite and comprehen- 
sible. 

" 2. To compare different groups by means of these 
simple pictures. Thus, two forests can only be com- 
pared by means of totals or averages of some sort. 

" 3. To obtain a picture of a complete group by the 
use of sample data only. An average obtained from a 
few hundred samples is so close to the exact average of 
the whole that the difference is negligible. 



252 THE ESSENTIALS OF LOGIC 

" 4. To give a mathematical concept to the relation* 
ship between different groups. We may say that the 
trees in one forest are taller than in another, but in 
order to find any definite ratio of heights, it is neces- 
sary to resort to averages." l 

The logic of such a situation is clear. In statistics, 
we stress the quantitative or measurable side of things ; 
and we take them, not as individuals, but as groups. 
The only way to institute a comparison is to reduce 
them to some common unit. What this common unit 
will be depends largely upon the purpose. We shall 
briefly describe the common averages used and point 
out their special value. 

The Arithmetical Average. The arithmetical 
average is the sum of the particular items divided by 
their number. By means of such an average, we are 
able to handle all the items as a single typical unit 
which we are able to compare with other like units. 
Thus, two football teams may be compared in regard 
to their weight by this means. Suppose the weights of 
the members of one team were 162, 180, 190, 155, 
170, 176, 182, 167, 205, 169, 158 pounds; then 
the average weight would be 174 pounds. The same 
method would be used to determine the average for the 
other team, and so a comparison could be instituted. 

It is obvious that such information as the above has 
its limitations. It makes a deal of difference where the 
weight in a team is distributed, and a general average 
for the whole group does not bring this out. Hence 
smaller groups are taken, such as the backfield or the 
line, and further comparisons instituted. The advan- 

1 King 1 , Elements of Statistics, p. 121. 



AVERAGES AND GRAPHS 253 

tages and disadvantages of the arithmetical average 
will be discussed later. 

The ' "Weighted ' Average. "By a 'weighted' 
average, we mean one whose constituent items have 
been multiplied by certain weights before being added, 
the sum thus obtained being divided by the sum of the 
weights instead of by the number of items." There are 
two types of weighted averages : one in which groups 
with varying numbers of members are already averaged 
and we desire to secure the arithmetical average for the 
groups taken together ; and the other in which the 
weights stand for estimates of relative importance. 

An example will make the first type clear. If, for 
example, a department store had seven departments 
and the average wage for each department was known, 
to obtain the weighted average it would be necessary 
to multiply the average wage for each department by 
the number of workers in it, add the results together, 
and divide by the total number of workers. 

The second type appears in the use of 4 index-num- 
bers ' which represent the estimated importance of the 
various groups. The following discussion by Bowley 
brings out very well the nature of the problem and the 
way in which it is met : — 

The classical and most useful application of weights 
is the formation of an index-number for the change of 
prices by fitting suitable weights to the changes meas- 
ured in the prices of various commodities. It is re- 
quired to find the change in the value of gold when 
measured by the prices of other commodities. Suppose 
that we are given that prices of certain commodities 
between two years were in the following ratios : — 



254 THE ESSENTIALS OF LOGIC 

Wheat Silver Meat Sugar Cotton 

First year 100 100 100 100 100 

Second year 77 60 90 40 85 

The simplest way to estimate for the general fall 
in price is to take the simple average of the numbers 
in the second year, viz., 70.4, and say that the general 
prices in the second year were 70.4 : 100 when ex- 
pressed in commodities. But it is at once clear that we 
cannot allow the commodities given to have equal influ- 
ences on the result; wheat is of greater importance 
than sugar and meat than silver; and again, we have 
taken arbitrarily three items to represent food and one 
for clothing; we need some means of deciding relative 
importance. Suppose we decide that wheat, cotton, 
meat, and sugar are respectively 7, 4, 3 times and 
twice as important as silver, we should get the follow- 
ing table : — 

*_* •SkSt* 1 JSft »■*- 

Wheat 77 7 539 

Silver 60 1 60 

Meat 90 3 270 

Sugar 40 2 80 

Cotton J*5 j* 340 

352 17 1289 

1289 
Weighted average is ... * == 75.8 

352 

Unweighted average is. . = 70.4 * 

5 

Weights are expressions of expert judgment and are 
to a certain extent relative. The logician must recog- 
nize that a possibility of error lies in their assignment. 

1 Bowley, Elements of Statistics, pp. 111-12, quoted from Jones. 



AVERAGES AND GRAPHS 255 

Fortunately, it can be demonstrated that an error in 
weights is less serious in its effects than a mistake in 
the size of the original items. 

The Mode. Another average which is very useful 
is the mode. It is variously defined as the most fre- 
quent size of item, the positions of greatest density, and 
the quantity which occurs with the greatest frequency. 
It is what we usually have in mind when we speak of 
4 the average man,' 4 the average income,' ' the average 
sized apple,' etc. We may say that the mode represents 
the type. 

The mode is not always easily determinable. When 
the case is simple, the mode can be determined by an 
examination of a frequency table. The following exam- 
ple should make the method clear : — 

Frequency Table showing Heights of Cornstalks 



ight in ft. (size of item) 


No. of stalks (frequency) 


m 


f 


3-4 


3 


4-5 


7 


5-6 


22 


6-7 


60 


7-8 


85 


8-9 


32 


9-10 


8 



n==217 

It will be noticed that size 7-8 is found 85 times, 
which is the greatest frequency, and is therefore the 
mode. There may be two or more frequencies with 
about equal claims to be the most usual occurrence. 
Such is the case in the variations of animal forms where 
one type shades continuously over into another. The 



25G THE ESSENTIALS OF LOGIC 

finer the grades, the easier it is to determine the domi- 
nant mode. 

The value of the mode comes out in the following 
examples : " The mode rather than the average in chest- 
measurements is the number most suitable for the 
ready-made clothier. For providing a post-office or a 
store, the mode in postal-orders or prices of tea needs 
to be known rather than any other average. Even the 
favorite coin in a collection may show the spirit of the 
congregation better than the arithmetic average of their 
contributions." 

The Median. The median is the middle quantity in 
a series. " If a number of similar objects are placed 
side by side in order of their size, they are said to be 
arrayed. If any group of objects is thus arrayed, the 
middle one is known as the median item." 

The median is of particular value when the data 
dealt with are not susceptible of measurement in defi- 
nite units. Psychological phenomena come in this class 
of material. " It is impossible to measure in specific 
units the mental characteristics of a child but it is per- 
fectly possible to array a group of children according 
to their respective mentality." 1 For this reason, the 
median was used by Francis Galton in his investiga- 
tions in inheritance and is being used in fields where 
quality can be graded in a series. 

The Geometric Average. The geometric average 
is obtained by multiplication of the n items of a series, 
and the extraction of the nth root of the produce. This 
average soon reaches a complexity which makes it im- 
possible of easy application for those not familiar with 

1 King, Elements of Statistics, p. 131. 



AVERAGES AND GRAPHS 257 

mathematics. Beyond the square and cube root, it in- 
volves the use of logarithms. It is very little used at 
the present. 

The Comparative Advantages of these Aver- 
ages. The mode is of advantage where we are not con- 
cerned with extreme variations which are few in num- 
ber, but with the type. Its disadvantage is that it is 
not always easy to determine. The median is easily lo- 
cated and can be determined for all data which can be 
arrayed in a series. Its chief advantage is that it is ap- 
plicable to relatively qualitative fields. The arithmetical 
average is readily calculated and gives weight to all the 
items; its chief disadvantage is that it requires the 
presence of all the items and even emphasizes the ex- 
tremes. The weighted average is a correction of the 
arithmetical when the series is made up of groups ; its 
chief importance, however, lies in its adaptation to the 
use of index-numbers. The average used in any con- 
crete investigation is determined by the character of 
the problem and the nature of the material. Often more 
than one average is calculated. 

Graphs and Graphical Methods. Diagrams are 
often employed to summarize tables in a picturesque 
and striking way. Various devices have been worked 
out to render the meaning of masses of figures clear 
and unambiguous. The following simple diagrams are 
often used in the exposition of statistical data : — 

1, Cartograms. Phenomena with a geographical 
location can be brought clearly before the eye by means 
of maps with devices to show variations. Colored print- 
ing is sometimes used, but, since this is expensive, va- 
rious modes of barring are employed. The rainfall maps 



258 THE ESSENTIALS OF LOGIC 

printed in the newspapers are good examples of this 
class. Another method is the use of dots to indicate the 
relative amount of the product under investigation, 
each dot standing for a given quantity. Such things as 
wheat and corn production can be represented in this 
way so that the results appeal directly to the eye. 

2. Pictograms. Pictures of comparative sizes, bar 
diagrams, block pictograms, and circles divided into 
segments are some of the devices used to bring data 
before the eye. The importance of such pictorial meth- 
ods for exposition can hardly be overestimated. "After 
a person has collected data and studied a proposition 
with great care so that his own mind is made up as to 
the best solution for the problem, he is apt to feel that 
his work is about completed. Usually, however, when 
his own mind is made up, his task is only half done. 
The larger and more difficult part of the work is to 
convince the minds of others that the proposed solution 
is the best one — that all the recommendations are 
really necessary." 1 One of the advantages of the 
graphic method is that the facts can be so presented 
that the reader can make deductions of his own. 

Experience has shown that some forms of charts are 
far superior to others and that faulty arrangements are 
easily adopted when criticism has not been directed 
against them. The bar method has many advantages 
in that it permits an exact estimation of the component 
parts and the use of colors to distinguish them. A 
development of the bar method by subdivision bars is 
shown in Fig. 15. 2 The sector method is widely used in 

1 Brinton, Graphic Methods for Presenting Facts, p. 1. 

2 Figures 15, 16, and 17, on pages 259, 260, 261, are taken from Brin- 
ton's Graphic Methods for Presenting Facts, by permission of the pub- 
lishers, The Engineering Magazine* 





£ *> 




H *»3 



fi 

M 

U°bl 

II 



-I 
M 

el 

li 



fi 



260 



THE ESSENTIALS OF LOGIC 



popular magazines ; its disadvantage lies in its lack of 
flexibility and the difficulty of arranging and lettering 
the sectors of the circle. Fig. 16, taken from The 
Survey, is a good example of pictorial presentation. 

In almost every chapter we have been compelled to 
stress the importance of analysis for thinking. What 
is called ' scientific management ' is beginning to point 
out its importance for social and industrial fields. The 
way in which the graphic method is being employed 
for this purpose is shown in Fig. 17, taken from System. 




Fig. 16. DISPOSITION OP A FAMILY INCOME OF FROM 
$900 TO $1000 

This cut shows an attempt to put figures in popular form. The eye is likely 
to judge by the size of the pictures rather than by the angles of the sectors. 




g | 

g s 

M 2 

2 s 

s 1 

Q ° 

125 

< 
3 






-a 

1 

A 



5 J 



a .a 



e 5 



262 THE ESSENTIALS OF LOGIC 

"Authority reaches down through the several branches 
of an organization like descent of blood, and, if prop- 
erly planned, it will be as irregular for a factor in an 
organization to be in doubt as to the person in authority 
over him as for the child to deny the parentage of his 
father. • . . It should be graphically shown what posi- 
tions are only temporarily filled, so that when new men 
are engaged they will fit into the scheme with functions 
planned, "* In such classification, we are dealing with 
parts of a system rather than with genera and species 
as in natural science. 

3. Frequency Graphs. Frequency tables are reduced 
to graphs in various ways. The foundation is the em- 
ployment of coordinates cutting each other at right 
angles at a point called the ' origin.' One set of data 
is measured along the axis of abscissae, while the other 
set is measured along the ordinate. A line drawn through 
points determined in this way is called a ' graph' and 
shows the essential points of the table. " For example, 
if the world's production of wheat over a number of 
years be plotted, a poor yield is represented by a de- 
pression, a rich one by a peak, a uniform one over 
several years by a horizontal line, and so on." It has 
been found that graphs dealing with different cases of 
the same phenomenon can be plotted on the same co- 
ordinates and so compared. Often considerable ingenu- 
ity is demanded before the graphs assume a form which 
lends itself to comparison. 

1 Brinton, Graphic Methods for Presenting Facts, p. 16. 



AVERAGES AND GRAPHS 263 

REFERENCES 

Bowley, Elements of Statistics. 

Brinton, Graphic Methods for Presenting Facts. 

Davenport, Statistical Methods with Special Reference to Biological 
Variation* 

Elderton, Primer of Statistics. 

Jones, Logic, Inductive and Deductive, pt. II, chap, n, and Sup- 
plement. 

King, Elements of Statistics. 



CHAPTER XXIII 

TESTIMONY AND CIRCUMSTANTIAL EVIDENCE 

Scientific Investigation vs. Judicial Proof. Thus 
far we have largely concerned ourselves with the meth- 
ods and logical processes of those investigations whose 
object is the discovery of laws and principles. Such 
investigations are essentially impersonal and theoretical. 
They can be carried on in the laboratory and the study, 
and there is usually less controversy in regard to the 
facts than in regard to the hypotheses to be erected 
upon them. Many seekers in the same field, having 
much the same training, accumulate facts by means of 
critical observation, and these facts are to furnish the 
foundation of the science. These accepted facts grad- 
ually converge in the direction of some satisfactory 
hypothesis, and so a law of nature or of society is tenta- 
tively established. We see, then, that science is coop- 
erative and largely impersonal, its data can be increased 
by recognized methods until they are sufficient, and it 
is not limited in the amount of time at its disposal. 
Nature is besieged rather than taken by storm. How 
long Newton worked before he published his results is 
well known, but it is not so well known that Darwin 
worked upon the development of his theory in regard 
to the origin of species for more than twenty years. 

But there is Another great field of systematic reason- 
ing which deserves the attention of the logician. If the 
methods and temper of the scientist have of late influ- 



CIRCUMSTANTIAL EVIDENCE 265 

enced the popular mind in the direction of greater care 
and exactitude, a similar influence has long been exerted 
by the methods and principles of legal reasoning. Sci- 
entific temper is paralleled in great measure by judicial 
temper. And we must remember that the situation in 
which legal reasoning is carried on is quite different 
from that in which scientific investigation takes place, 
and is much less favorable to good reasoning. The air 
is full of contention and of the personal element, the 
time in which to reach a decision is limited, and the 
necessary facts are often hard to find and verify. Judi- 
cial proof is less creative than scientific investigation, 
but it is in many ways more difficult. 

The Difficulties confronting Judicial Proof. The 
difficulties confronting judicial proof are very similar 
to those which arise in practical life when the problem 
is controversial in character. The juror is not in a posi- 
tion to observe the facts, but must reach his decision 
through the testimony of others and through inference 
from what is called 'circumstantial evidence.' The sci- 
entific investigator can repeat his facts at wish, but this 
the juror, no more than the historian, can do. " The 
same combination of circumstances which go to make 
up a case of crime cannot, where they are at all numer- 
ous, be expected to occur again. And even if it could or 
did occur, it would answer no purpose ; for it is the 
identical transaction which took place, and as it took 
place, which is to be the sole subject of inquiry." 1 The 
juror's observation is of an indirect, dependent, and 
therefore inferior kind. Again, the original observer of 
the facts was seldom aware of their importance. " Many 

1 Burrill, A Treatise on Circumstantial Evidence, p. 94. 



266 THE ESSENTIALS OF LOGIC 

of the facts . . . not only present themselves to the 
senses, incidentally, unexpectedly, and transiently, but 
are, outwardly, and as they present themselves, of the 
most ordinary and familiar kind, having nothing on 
their face to attract or arrest attention in any consider- 
able degree ; and not to be distinguished from the great 
mass of facts and events which are constantly passing 
before the eyes of men, in their daily intercourse with 
each other. Hence, where they are perceived merely by 
the organs of sense, without any act on the part of the 
observer, to give them connection with himself, they 
are usually perceived in a general and superficial man- 
ner." Thus, there is a large amount of possible error 
in this incomplete and indirect observation upon which, 
as a foundation, the juror must build his construction 
of the case. The court must be certain of the identity 
of the witness and of his general competency, that he 
was actually an observer of what he testifies to, that 
his testimony is not biased, etc. Finally, the juror must 
be able to mass all this evidence, much of which is con- 
flicting, together and draw a conclusion which seems to 
him to explain the facts of the case. He is compelled to 
pass judgment after judgment and then to estimate 
the comparative value of these integral yet subordinate 
conclusions in a total view of the problem. Neither the 
steps nor the final synthesis is easy of accomplishment 
in complex cases. 

Distinction between Circumstantial and Testi- 
monial Evidence. All evidence involves an inference 
from some fact to the proposition to be proved. To be 
evidence, a fact must have a recognizable bearing upon 
the issue or probandum. In such a bearing lies its rel- 



CIRCUMSTANTIAL EVIDENCE 267 

evance. Evidence divides itself into two classes, called 
respectively ' direct ' or i testimonial evidence ' and 6 cir- 
cumstantial evidence.' The distinction between these 
two types is as follows : Direct or testimonial evidence 
consists of information derived from assertions made 
by those who have actual knowledge of the fact ; cir- 
cumstantial evidence consists of facts from which in- 
ferences to the principal fact can be drawn. Thus, 
testimonial evidence is made up of the assertions of 
witnesses who are presumed to have first-hand knowledge 
of the fact at issue, while circumstantial evidence con- 
sists of * circumstances ' from which the fact at issue 
can be inferred according to known laws. It must be 
remembered, however, that these * circumstances ' must 
themselves be proved by testimony. 

The Nature of Circumstantial Evidence. It is 
obvious that circumstantial evidence gains its chief im- 
portance as supplementary to direct evidence. A com- 
mon direction for these two kinds of evidence is almost 
bound to carry conviction. Thus, there may be only one 
witness who testifies to having seen a crime committed, 
while many may have seen the accused near the place 
and showing signs of agitation or marks which fit in 
with the inference suggested by the prosecution. Thus, 
testimonial and circumstantial evidence are usually in- 
tertwined. But cases occur in which there is no direct 
evidence, i.e., in which no one has witnessed the com- 
mission of the crime. At such times, reliance must be 
placed wholly upon inference from circumstances. For 
instance : " A house has been robbed. All the property 
stolen from it is found directly after the robbery in the 
possession of A. Besides this, at the time when the 



268 THE ESSENTIALS OF LOGIC 

robbery is discovered, a hat, usually worn by A, is found 
in the house. It is almost certain as a general proposi- 
tion, that any man of whom these facts are true, must 
be the robber. And assuming it to be conclusively 
established that both these facts are true of A, we may 
conclude with an approach to absolute certainty that A 
is guilty of the robbery." When we come to examine 
all such cases of circumstantial evidence, we find that 
the principle of explanation is the same as that used in 
science. Given certain facts, we must form an hypothe- 
sis to explain them. In a case like the above, the 
hypothesis that A is the robber is the one that naturally 
occurs. We are certain, at least, that if he is not the 
robber, he must know who the robber is. From the 
standpoint of logic, the proof of the hypothesis consists 
in the elimination of all alternative possibilities. The 
student will recall that Mill's Methods depended largely 
upon the scientist's ability to exclude possible causes 
and so narrow down the field. 

The Convergence of Evidence. It is seldom that 
a single circumstance is given such value as to be re- 
garded as conclusive. One instance occurred which 
should serve to put us on our guard against the easy 
assumption that there is no other possible hypothesis 
but the one which most naturally occurs to us. " A man 
was convicted and executed for stealing a horse, on the 
strength of the presumption of the animal's being found 
in his possession on the same day on which it was stolen ; 
but it afterwards appeared that the real thief, being 
closely pursued by the officers of the law, had met the 
unfortunate man, to whom he was a total stranger, and 
requested him to walk his horse for him for a while. 



CIRCUMSTANTIAL EVIDENCE 269 

He had then escaped." In practically all cases, then, 
the prosecution builds up a framework of evidence 
which converges on the hypothesis that the accused is the 
guilty man. The two facts to be connected are the 
crime and the individual charged with its commission. 
The evidentiary facts are shown to converge upon such 
a suggested connection. The figure most frequently em- 
ployed is that of a chain, but the analogy has a weak- 
ness so far as it implies that the disproof of a single 
link will break the chain. As a matter of fact, the con- 
nection is more like a cable woven of strands than a 
single chain. When each single inference from a circum- 
stance to the issue is probable, the combination of these 
separate probabilities may lead to a moral certainty 
through the impossibility of finding an hypothesis, other 
than the one championed, which will cover them all. 
The defense then tries to break down the framework 
of evidence by trying to disprove certain of the alleged 
facts, by attempting to show that the interpretation of 
other facts is false, and, in short, by seeking to bring 
forward another hypothesis as an explanation. And so 
the struggle between the two sides continues, with the 
jury as the deciding body. 

Direct or Testimonial Evidence. When we are 
dealing with past events, as in a case of crime and in 
history, we are compelled to rest our beliefs upon some 
sort of testimony. Testimony, if true, enables us to reap 
the results of the perceptions of others, to see indirectly 
with their eyes. Hence, testimony has an unique value. 
But it has also its dangers against which the whole 
procedure of historical investigation and the theory of 
judicial proof are directed. It is a far cry from the naive 



270 THE ESSENTIALS OF LOGIC 

credulity of the child to the methodical skepticism of the 
trained historian and the legal expert ; yet experience 
of error has forced this change. " Our first natural 
attitude toward testimony is one of trust ; not because 
we have reasoned that it is trustworthy, but merely be- 
cause we cannot help it. If it had not always been 
natural to accept the statements of those about us as 
substantially true, we should probably not be alive now 
to discuss the matter ; for the telling of the truth on the 
one hand and confidence in the story told on the other 
are very important means for the preservation of the 
race." 1 But experience soon qualifies this tendency. 
We discover that we must hear as much evidence as we 
can, and then compare, sift, and weigh it. Such collection, 
sifting, and comparing is at first rough and ready. It is 
soon developed into a careful technique with accepted 
principles and maxims. The two best examples of such 
technique are, of course, historical method and legal 
method. We shall, in the main, concern ourselves with 
the principles of legal method, but shall now and then 
call attention to historical method and its manner of 
dealing with the documents of the past. 

The Modern Critical Attitude toward Testi- 
mony. " Any assertion, taken as the basis of an in- 
ference to the existence of the matter asserted, is testi- 
mony, whether made in court or not. Assertions made 
on the witness stand are merely the commonest class of 
testimonial evidence." 2 Such assertions are, then, the 
raw material of proof. They must be tested until a 
residuum is left as morally certain fact. 

1 Aikins, The Principles of Logic, p. 364. 

2 Wigmore, Principles of Judicial Proof p. 312. 



CIRCUMSTANTIAL EVIDENCE 271 

When a witness's assertion is examined from the 
logical standpoint, it is seen to involve at least three 
elements, perception, memory, and narration. In the 
chapter dealing with " Observation and Fact," we be- 
came aware of the ever-present danger of error in 
both observation and memory. What was said then 
could be reinforced by case after case in the annals of 
law. 1 

" A thousand mistakes of every description would be 
avoided if people did not base their conclusions upon prem- 
ises furnished by others, take as established fact what is 
only possibility, or as a constantly recurring incident 
what has only been observed once. ... I am assuming 
that the witness is really desirous of speaking the truth 
and is merely a bad observer." 2 Much testimony can be 
proved to be mistaken by fairly simple tests. " Suppose 
a witness affirms that he was beaten by Hiov ten min- 
utes. Let a watch be placed before him and ask him to 
take good note of how long ten minutes lasts and then say 
whether it was really ten minutes. After a quarter of 
a minute he will exclaim, ' It certainly did not last 
longer than that.' " 

Cross-examination is often of great assistance in 
determining the validity of assertions. New statements 
may be made by the witness which will disagree 
with his other statements, or further developments 
may be indicated. " In Lincoln's first murder trial, 
the chief witness had testified to seeing the murder 
committed by the prisoner. In the cross-examination he 
added a number of details : that the shooting was at 

1 See Wigmore, Principles of Judicial Proof pp. 296-726. 

2 Hans Gross, Criminal Investigation, p. 22. 



272 THE ESSENTIALS OF LOGIC 

ten o'clock at night ; in beech timber ; in August ; 
that he was twenty feet or more away ; that he could 
see the pistol and how it hung ; that the nearest lights 
were half a mile away, and that he saw it all by moon- 
light. Lincoln showed that the moon did not rise till 
one o'clock in the morning. Cross-examination may 
bring out inconsistencies due to dishonesty as well as 
incompetence, as shown in this example." 1 

Logic has little concern with the practical difficulties 
due to the temperament of the witness. There are 
dull and stupid witnesses, timid and self-conscious, 
hostile, dogged, etc. Logic must, however, stress 
the part played by suggestion, and the difficulty 
many people have of expressing themselves adequately. 
The exhaustive study of testimony in the modern 
schools of scientific law calls logic, ethics, anthropology 
experimental psychology, and psychiatry to its aid. 
Race, age, sex, mental disease, moral character, feeling, 
interest, and experience, all affect the character of the 
testimony given. 

After the identity of the witness has been estab- 
lished, the first problem is : Was the witness in a posi- 
tion to perceive the facts ? The court wishes to know 
the witness's opportunities. Next comes the question 
whether he has any strong bias or motive for falsifying. 
Very often the testimony of interested parties is re- 
jected; it is at least somewhat discounted. When the 
testimony given is against the advantage of the witness, 
it is, however, regarded as having peculiar weight. 
Such testimony usually occurs under cross-examina- 
tion. 

1 Quoted from Jones, Logic, Inductive and Deductive, p. 272. 



CIRCUMSTANTIAL EVIDENCE 273 

Logical Standards and Tests. There are certain 
logical tests which are directly applicable to the story- 
told by a witness. It must be self consistent ; it must be 
consistent with other known facts of the case; and 
must be consistent with the larger run of human ex- 
perience. Let us look at these three logical tests some- 
what closely. 

To be acceptable, the testimony of a witness must 
be coherent and self-consistent. When two of his asser- 
tions are shown to conflict, not only are we unable to 
decide which is the true one, but we are also rightly in- 
clined to be suspicious of the rest of his story. 

Again, if the story told conflicts with facts which 
are otherwise known beyond reasonable doubt, doubt is 
thereby cast upon it. This is especially the case where 
the facts are important and conspicuous. The agree- 
ment or disagreement of the particular testimony with 
that advanced by other witnesses enters here as con- 
tradiction or convergent confirmation. 

Lastly, the statements made must not conflict with 
the laws of nature or with the tested possibilities of 
the case. When a man testifies that he saw clearly 
what occurred in a darkened room when he was look- 
ing in from outside, we have good reason to reject his 
testimony. Of course, assertions must not be too lightly 
and hastily rejected. 

These three tests imply both internal and external 
evidence. A very good example from history of their 
application is the determination of the false authorship 
of the Donation of Constantine. This famous docu- 
ment was the supposed grant by the Emperor Constan- 
tine to Pope Silvester and his successors, not only of 



£74 THE ESSENTIALS OF LOGIC 

spiritual supremacy over the other great patriarchates 
and over all matters of faith and worship, but also of 
temporal dominion over Eome and Italy and the prov- 
inces, places, and civitates of the western regions. A 
close study of the document, including the style, lan- 
guage, and references, has convinced scholars, both 
Catholic and Protestant, that the document is a forgery 
dating from the eighth century. This painstaking ap- 
plication of internal and external evidence has been 
applied to the Old and New Testament, and is usually 
called the 4 Higher Criticism.' It is very seldom that 
the alleged author turns out to be the real author. 

The Movement of Judicial Proof. Having exam- 
ined the nature of both circumstantial and testimonial 
evidence, it may be well to glance at a summary state- 
ment of the actual movement of evidence and argument. 
We shall refer to the asserter of the fact as the * Pro- 
ponent' and the opposer as the ; Opponent.' In the 

following outline, the sign ^> signifies ' tends to 

prove ' ; the sign o — >> signifies ' tends to dis- 
prove ' ; the sign <^ signifies ' explains away ' ; letter 
T stands for a testimonial evidential fact; letter C 
stands for a circumstantial evidential fact. 

Circumstantial Evidence Process 

Prohandum : X stabbed Y with a knife at a certain time and 
place. 
Proponent's Evidential Fact — C= Bloody knife was found on 

X > Prohandum. 

Proponent's Evidential Fact ex- 
plained by Opponent — C = X drew it from the wound 

after the fray on coming 
to Y *s assistance < Pro- 
ponent's Evidential Fact. 



\ 



CIRCUMSTANTIAL EVIDENCE 275 

or,— 
Proponent's Evidential Fact de- 
nied by Opponent — C = Bloody knife was not found 

on X — o — > Propo- 
nent's Evidential Fact, 
and this the opponent may do, either — 

(1) by adducing new evidential 

facts — T=M's assertion that on 

searching X no knife 
was found. 
C = No trace of blood from the 
knife appeared on X's 
garments. 

(2) or by questioning the inference from the T or C on which 
Proponent's Evidential Fact itself rested as a probandum. 

Finally, — 
Eival New Facts adduced by 

Opponent — C=.X had no quarrel or other 

motive to stab Y — o — > 
Probandum. 
and T= N a bystander asserts that 
X did not stab Y — o — > 
Probandum. 1 

The Massing of Mixed Evidence. In any com- 
plex case, a huge mass of more or less conflicting evi- 
dence is presented to the juror's mind, and he must 
arrange it in such a way as to weigh it correctly. 
" Many data, perhaps multifarious, are thrust upon us 
as tending to produce belief or disbelief. Each of them 
(by hypothesis) has some probative bearing. Conse- 
quently, we should not permit ourselves to reach a con- 
clusion without considering all of them and the relative 
value of each." What the mind ordinarily does under 
such cases is to pass back and forth from significant 

1 Adapted from Wigmore, Principles of Judicial Proof p. 26. 



276 THE ESSENTIALS OF LOGIC 

fact to significant fact allowing itself to balance one 
fact against another. The result is a drift in a certain 
direction. In this way, a series of subordinate judg- 
ments is passed, and these prepare the field for more 
comprehensive judgments of a final sort. The mind 
then goes back over the material in the light of its ten- 
tative decision to see whether all the facts fall into line. 
If they do, the decision is accepted as final. The fun- 
damental mental necessity is the ability to coordinate 
the data and weigh them in their relation to one an- 
other. Along with this must go openness of mind and 
willingness to go back and forth over the facts with 
all the reasonable hypotheses in mind to see how ade- 
quately they fit. 

In such complex reasoning the strands of argument 
are so many and so interwoven that fallacies of one 
kind or another are almost sure to creep in unless the 
utmost vigilance is exercised. Neglect of other possi- 
bilities, false disjunction, false analogy, argumentum 
ad populum are fairly common features of forensic 
contests. In summing up, however, the fallacy which 
should be most zealously guarded against is the fallacy 
of the ' neglected aspect/ It is so easy to assume that 
all the relevant factors have been taken into account 
and have been given their due weight ; yet nothing is 
more common than to over-simplify a problem and to 
neglect important causes and facts. How many of us 
have committed this fallacy of neglected aspect in con- 
nection with the European War or in connection with 
social problems like poverty and drunkenness ! 

The following newspaper argument against prohibi- 
tion illustrates this tendency very well : " You destroy 



CIRCUMSTANTIAL EVIDENCE 277 

the jobs of people upon whom about 5000 of the popu- 
lation depend; you take the jobs away from about 
2000 room-rent or house-rent payers or home-owners ; 
you deprive the city itself of about 1300,000 of direct 
revenue, in the way of excise taxes and property taxes ; 
you depreciate the rental value of about 15,000,000 
worth of property in the town." Granted that the as- 
sertions are correct, " if the facts which they bring for- 
ward were the only ones to be considered, the inference 
as to prohibition would be inevitable. If, however, the 
liquor traffic is as pernicious in its influence as its op- 
ponents claim it to be, the benefits which result from it 
are far outweighed by the evil it produces. This aspect 
of the case is neglected however, and so the argument 
remains inconclusive." * 

REFERENCES 

Aikins, The Principles of Logic, chap. xxxv. 

Bode, An Outline of Logic, chap. xn. 

Hibben, Logic, Deductive and Inductive, chap. xiv. 

Jones, Logic, Inductive and Deductive, pt. m, chap. in. 

Wigmore, Principles of Judicial Proof, Introductory, and passim, 

1 Bode, An Outline of Logic, p. 196. 



CHAPTER XXIV 

EXPLANATION AND SYSTEM-FORMATION 

The Nature of Explanation. To explain any- 
thing is to show that it follows from something else 
already known, A fact is explained when it is inter- 
preted by means of a law or a principle. The specific 
is explained by the general ; and the less general by 
the more general. In explanation, we move downward 
from rules to cases, from principles to their exemplifi- 
cations. We see the temporary and the changing in 
the light of the more permanent and relatively un- 
changing. 

That all explanation is in its essence deduction 1 has 
been generally recognized by logicians. We try to re- 
late the given to those generalizations which we have 
slowly worked out as both rules of action and rules of 
interpretation. We are not comfortable with mere 
facts which are unordered and unrelated. They challenge 
us as chaotic and meaningless until we can somehow 
put them together as parts of a permanent whole which 
can be conceived. Thus, in the domain of the physical 
sciences, a fact is felt to be explained when it is re- 
lated to the terms of a general principle. 

The Sentiment of Rationality. A given fact by 
itself seems like a shot out of a pistol. It is, — our 
senses are, perhaps, witnesses to its occurrence, — but 
it stands in isolation. So far as this is the case, our 

1 Sigwart, Logic, vol. II, p. 417. 



EXPLANATION AND SYSTEM-FORMATION 279 

minds cannot really grasp it and give it meaning for the 
simple reason that past experience cannot be brought to 
bear upon it. It remains, then, a brute sensational event 
to which our concepts cannot attach themselves. But 
because our minds try to find some point of attachment, 
some way of striking up a friendship with the event, 
they feel baffled and uncomfortable. Thus, the senti- 
ment of rationality, the desire to explain and interpret, 
is an expression of the very mode of working of human 
consciousness. When any event or thing is given, our 
minds seek to find relations between it and other facts 
already familiar and more or less interpreted. In this 
way it is assimilated and given a local habitation and a 
name. " All knowledge, all science, thus aims to grasp 
the meaning of objects and events, and this process 
always consists in taking them out of their apparent 
brute isolation as events, and finding them to be parts 
of some larger whole, suggested by them, which, in 
turn, accounts for, explains, interprets them; i.e., 
renders them significant. Suppose that a stone with 
peculiar markings has been found. What do these 
scratches mean ? So far as the object forces the rais- 
ing of this question, it is not understood ; while so far 
as the color and form that we see mean to us a stone, 
the object is understood. It is such peculiar combina- 
tions of the understood and the non-understood that 
provoke thought. If at the end of the inquiry, the 
markings are decided to mean glacial scratches, obscure 
and perplexing traits have been translated into mean- 
ings already understood : namely, the moving and 
grinding power of large bodies of ice and the friction 
thus induced of one rock upon another. Something 



280 THE ESSENTIALS OF LOGIC 

already understood in one situation has been transferred 
and applied to what is strange and perplexing in an- 
other, and thereby the latter has become plain and 
familiar, i.e., understood. This summary illustration 
discloses that our power to think effectively depends 
upon possession of a capital fund of meanings which 
may be applied when desired" l 

The Role of Concepts. Concepts play a tremen- 
dously important part in both reasoning and explana- 
tion. Let us try- to bring out the deductive side of 
explanation referred to above by stressing the role of 
concepts in experience. Because concepts are accepted 
organizations of experience, anything related to them is 
naturalized, so to speak, and becomes, thenceforth, a 
citizen of the mind. Relation to the concepts gives it 
its credentials. Thus the foundation of all explanation 
is the capacity of the mind to generalize and to secure 
by means of analysis, abstraction and synthetic imagin- 
ation those general ideas and principles which illumin- 
ate and organize experience. Our study of induction 
has been essentially a tracing of the steps and activities 
involved in the attainment of such concepts. We have 
seen how facts are observed and selected at the instance 
of some problem, how comparisons and analyses are 
made, how guesses at the causes or principles at work 
are made by fertile minds, how these guesses are tested 
and modified and re-tested, how systems of conceptual 
knowledge slowly arise and are used to give meaning 
to new facts as well as to the old from which they 
sprung. Now it is to this property of such conceptual 
systems to give meaning to new facts that we are call- 

1 Dewey, How We Think, pp. 117-18. 



EXPLANATION AND SYSTEM-FORMATION 281 

ing attention. It is in this property that explanation 
consists. 

It is significant that this explanatory property of 
concepts can be connected with the syllogism. It will 
be remembered that the typical syllogism has a univer- 
sal proposition for its major premise. The minor pre- 
mise then states a concrete case which can be subsumed 
under the universal principle, while the conclusion con- 
sists of the actual identification of the concrete case 
with the principle. 

All cases of M are cases of P;' 
S is a case of M; 
Therefore S is a case of P. 

Both M and JP are abstract characters or universals; 
they are concepts which have gradually been achieved 
by the human mind as the result of that sentiment of 
rationality to which we have referred above. " This is, 
in fact, a world in which general laws obtain, in which 
universal propositions are true, and in which reasoning 
is therefore possible." We reason down from such 
general concepts to facts and thereby explain them. 

Concepts are " instruments (1) of identification ; 
(2) of supplementation ; and (3) of placing in a sys- 
tem. Suppose a little speck of light hitherto unseen is 
detected in the heavens. Unless there is a store of 
meanings to fall back upon as tools of inquiry and 
reasoning, that speck of light will remain just what it 
is to the senses — a mere speck of light. For all that 
it leads to, it might as well be a mere irritation of the 
optic nerve. Given the stock of meanings acquired in 
prior experience, this speck of light is mentally attacked 
by means of appropriate concepts. Does it indicate 



282 THE ESSENTIALS OF LOGIC 

asteroid, or comet, or a new-forming sun, or a nebula 
resulting from some cosmic collision or disintegration ? 
Each of these conceptions has its own specific and dif- 
ferentiating characters, which are then sought for by 
minute and persistent inquiry. As a result, then, the 
speck is identified, we will say, as a comet. Through a 
standard meaning, it gets identity and stability of 
character. Supplementation then takes place. All the 
known qualities of comets are read into this particular 
thing, even though they have not been as yet observed. 
All that astronomers of the past have learned about 
the paths and structure of comets becomes available 
capital with which to interpret the speck of light. 
Finally, this comet-meaning is itself not isolated ; it is 
a related portion of the whole system of astronomic 
knowledge. Suns, planets, satellites, nebulas, comets, 
meteors, star-dust — all these conceptions have a cer- 
tain mutuality of reference and interaction, and when 
the speck of light is identified as meaning a comet, it 
is at once adopted as a full member in this vast king- 
dom of beliefs." 1 A fact which is identified, supple- 
mented in this broad way, and put into a system is 
explained ; it has been removed from its isolation, 
given relations to other things, and interpreted by 
general principles. 

Proof and Explanation. A proposition is proved 
when it is shown to follow from accepted premises, 
while a fact or specific rule is explained when it is 
shown to be the natural consequence of principles. It 
is evident that proof and explanation are essentially the 
same ; in both the deductive element dominates. Thus 
1 Dewey, How We Think, pp. 126-27. 



EXPLANATION AND SYSTEM-FORMATION 283 

far we have looked at the problem mainly from the 
angle of explanation ; let us now examine it from the 
side of proof. Why does the application of the major 
premise to a case constitute proof ? " The answer is 
that it serves to connect the conclusion with the system 
of concepts or general principles that have previously 
been accepted. When one sees that the new suggestion 
comes under the old principles, the belief that has been 
developed for the system of knowledge extends to the 
particular instance. The laws and principles that have 
been established and accepted are connected with the 
conclusion that is in doubt, and the doubt disappears. 
Each doubt that is solved increases the belief in the 
principle, since it assures its connection with a new 
fact. It should be added that the process of reference 
to the system of knowledge, not merely justifies the old, 
but also increases the number of applications of the 
old. It extends its application, and when the conclu- 
sion itself is confirmed in practice, the general principle 
receives new warrant." 1 This quotation brings out ad- 
mirably the fact that knowledge consists of the growth 
of systems of knowledge which must take up new facts 
into themselves. Such systems possess mental author- 
ity, and proof is the expression of this authority. 
Combined with such authority there must exist the 
mental perception of the inner coherence of system and 
fact. The system must be capable of assimilating the 
fact ; it is here that the deductive element enters. 

Systems are tentative. Systems are no longer re- 
garded as having either their final form or content. 
There is less dogmatism in all fields to-day than formerly. 

1 Pillsbury, Essentials of Psychology, pp. 234-35. 



284 THE ESSENTIALS OF LOGIC 

The trial-and-error feature of knowledge is more clearly 
recognized. We may allow ourselves to speak of sys- 
tems of knowledge as growths, but we must not be mis- 
led by the organic analogy. There are differences as 
well as similarities between the growth of systems of 
ideas and the growth of organisms. The difference I 
would stress lies in this, that the innate or determined 
factor is less obviously in control in systems of knowl- 
edge than in the growth of a particular organism. To 
put this point concretely, systems of knowledge do not 
have an heredity. If we desire an analogy, it is far 
better to compare the development of knowledge in a 
particular field with the adaptation of a human being 
to his environment. Habits are necessarily tentative and 
revocable just as ideas are. Man has found that he 
must relinquish habits and customs and institutions, 
much as he is forced at times to give up ideas once 
fondly cherished. In both domains, however, we have 
good reason to believe that it is not a case of mere 
supplanting, but that there is a genuine advance, a 
real progress. I cannot do better in this connection 
than to quote what Bertrand Russell writes in regard 
to the attitude and contributions of Henri Poincare to 
modern science : " Another reason which makes a phi- 
losophy of science specially useful at the present time 
is the revolutionary progress, the sweeping-away of 
what had seemed fixed landmarks, which has so far 
characterized this century, especially in physics. The 
conception of the 4 working hypothesis,' provisional, 
approximate, and merely useful, has more and more 
pushed aside the comfortable eighteenth-century con- 
ception of ' laws of nature.' Even the Newtonian dy- 



EXPLANATION AND SYSTEM-FOEMATION 285 

namics, which for over two hundred years had seemed 
to embody a definite conquest, must now be regarded 
as doubtful, and as probably only a first rough sketch 
of the ways of matter. And thus, in virtue of the very 
rapidity of our progress, a new theory of knowledge has 
to be sought, more tentative and more modest than that 
of more confident but less successful generations." x 

Levels of Explanation. We may distinguish dif- 
ferent levels in explanations. The first stage is classifi- 
cation. The dominant purpose at this level is to gather 
objects, compare them, and, finally, classify them. When 
systems of classification are worked out, specimens can 
be ordered in relation to one another and new cases 
can be identified and put in their proper place. No 
matter how external and superficial such systems of 
classification are, they represent the beginning of sci- 
entific explanation ; things are removed from their iso- 
lation. As the system of classification is penetrated by 
perception of more essential characteristics, this stage 
passes to the next, which may be called * the empirical/ 

At the empirical level, subordinate laws and princi- 
ples are discovered. For example, many strands of cau- 
sal uniformity and laws of action and reaction become 
known. In medicine, it is discovered that certain drugs 
have definite effects upon the organism, and that the 
individual reacts in certain ways to various toxins. In 
chemistry, laws and principles are often known while 
there is doubt of their real significance. One of the 
best historical instances of the empirical stage is the 
situation in astronomy after Kepler and before New- 
ton. Kepler discovered that the planetary orbits are 
1 Russell, Preface to Poincar^'s Science and Method, pp. 6-7. 



286 THE ESSENTIALS OF LOGIC 

elliptical instead of circular as had been supposed. 
Kepler generalized the known facts in terms of his 
three laws : (1) that the planets move in ellipses round 
the sun, with the sun in one of the foci ; (2) that they 
describe equal areas in equal times ; (3) that the cubes 
of their mean distances vary as the squares of their 
periodic times. Although many suggestions were made 
and analysis of motion was carried further by various 
physicists, it remained to Newton to carry astronomy 
over to the third level, that of explanation proper. 

Newton did two things : " He conceived that the 
force which deflected the planets into their orbits was 
the same as that which made bodies fall to the earth ; 
or, to put it differently, he identified celestial attraction 
with terrestrial gravity, and conceived the earth as es- 
sentially falling out of a straight path towards the sun, 
and the moon towards the earth ; and he invented a 
mathematical calculus by which he could work out 
what were the theoretical consequences of the princi- 
ples he assumed" 1 Examining these two things which 
Newton accomplished, we see that they were, first, an 
extension of the idea of gravity to all cases of physical 
bodies, an act of universalization, and second, the en- 
trance of a distinctly deductive element. The more de- 
duction increases, the more has the level of explanation 
been achieved. 

The ideal often held by the physical sciences is well 
expressed by Helmholtz. In his little book on the Con- 
servation of Force, he writes : " So that at last the task 
of Physics resolves itself into this, to refer phenomena 
to inalterable attractive and repulsive forces whose in- 

1 Joseph, An Introduction to Logic, p. 479. 



EXPLANATION AND SYSTEM-FORMATION 287 

tensity varies with distance. The solution of this task 
would at the same time be the condition of Nature s 
complete intelligibility ." For Helmholtz, in other words, 
partial explanations in science must be subsumed under 
completer, more deductive ones until the ideal he sets 
forth is reached. This is not the place to discuss this 
ideal from the philosophical side. It may be of interest 
to the student, however, to point out that it is a clear 
statement of the mechanical view of the world. 

General Explanation and Specific Explanation. 
Sometimes the scientist is primarily interested in dis- 
covering general laws and then carrying these laws 
themselves back to still more general principles ; at 
other times, he wishes to explain particular facts. The 
more concrete the science, the more is there an interest 
in the particular for its own sake. Thus, history is 
mainly concerned with events or customs which have 
been brought about by the interaction of many forces 
and agencies. Such events cannot be deduced from ele- 
mentary and universal principles. There is not repeti- 
tion enough, and the factors concerned are too complex 
and mutable. Where deduction can afford genuine 
prediction, there must be relative simplicity. It is pos- 
sible to predict the transit of Venus, the effect of Ice- 
land spar upon a beam of light, and the product of the 
union of hydrogen and oxygen ; but it is impossible to 
predict what will happen after the present great war. 
The historian must grope his way to generalizations 
which are only tendencies ; his chief interest must be 
directed to the understanding of events which have al- 
ready happened by tracing their known antecedents. 
But when the physical scientist seeks to understand just 



288 THE ESSENTIALS OF LOGIC 

why some specific event happened, he, also, must search 
out all the relevant circumstances. The main difference 
is that time is a less important factor for him than it is for 
the historian. In fact, as we pass from the abstract sci- 
ences through the biological to the human sciences, time 
increases in importance. Institutions and events are 
best interpreted when we know how they arose. Our 
conclusion is, that sciences differ in their emphases. 
Some, the more abstract, aim to furnish general prin- 
ciples only and leave the specific and the unique to the 
concreter sciences ; while the more concrete sciences de- 
vote much of their attention to particular events which 
are judged to be important. 

Typical Systems of Knowledge. Many logicians 
have attempted to classify the sciences according to 
some one principle. Such classifications must, however, 
be recognized to be relative to the principle adopted. 
Suppose that we use the relative proportion of general 
law and specific fact as the standard of division. We 
shall then commence with mathematics, pass to me- 
chanics, thence to chemistry ; from chemistry we shall 
go to biology and psychology, and, finally, to the 
human sciences which all involve the methods of his- 
tory. Corresponding to such a passage from the more 
abstract to the more concrete is a change in the nature 
of the material studied. We begin with the abstract 
properties of physical things and end with highly or- 
ganized and changing wholes. Let us glance briefly at 
the two extremes to see what the respective systems are 
like and how they are developed. 

Mathematics is a typical deductive science. It does 
not involve an appeal to particular facts which must be 



EXPLANATION AND SYSTEM-FORMATION 289 

generalized. Geometry, for example, does not begin with 
concrete things as do the physical sciences, but with 
certain concepts, given in definitions, axioms, and pos- 
tulates, and with the nature of abstract space. " It is 
because space relations are unaffected by locality that 
what I have seen to be a property of this circle must 
be a property of any circle." * What mathematics rests 
on, then, is an apprehension of the relations between 
the elements of space and quantity. In a very real sense, 
there are no particular instances which have relevant 
qualities of their own. Thus, the data of mathematics 
are few in number and essentially changeless, ichich is 
another way of saying that they are conceptual rather 
than perceptual. The generalization-aspect of the sci- 
ence is taken care of at the very start. It follows that 
the test of the truth of any conclusion cannot be of a 
perceptual character; rather is it of the nature of a 
recognized agreement with the principles and theorems 
already developed. A geometrical system is primarily a 
realm of internal consistency. " Thus the space-intui- 
tion which is so essential an aid to the study of logic 
is logically irrelevant : it does not enter into the prem- 
ises when they are properly stated, nor into any step 
of the reasoning," 2 The true method of studying geom- 
etry is to conceive "interesting simple figures, such 
as the triangle, the parallelogram, and the circle, and 
to investigate the correlations between their various 
parts. The geometer has in his mind not a detached 
proposition, but a figure with its various parts mutually 

1 Joseph, An Introduction to Logic, p. 506. Mr. Joseph's chapter on 
44 Mathematical Reasoning " is well worth study. 

2 Whitehead, Introduction to Mathematics, p. 242. 



290 THE ESSENTIALS OF LOGIC 

inter-dependent." 1 Such figures are seen in the light 
of the primary set of axioms and postulates. We may 
say, then, that mathematics deals with abstract entities 
which are conceived. 

The historical sciences, on the other hand, are founded 
on concrete data. These data may be classified into two 
groups, material facts and testimony. The first duty 
of the historian is to gather all the data available. As 
a rule, such data consist of documents, which are records 
in various forms of the thoughts and actions of men of 
former times. 2 No one who has not given some thought 
to the matter can appreciate the effort required to 
bring about even a partially satisfactory fund of mate- 
rial, especially where the very distant past is concerned. 
The next step is the estimation of the relative value 
of the various items. It is to this problem that much 
of the historian's ingenuity is directed. Both internal 
and external evidence must be adduced, analyses made, 
and exact scholarship brought to bear. As material is 
evaluated, a certain body of more or less certain fact is 
established and worked up into an interpretative narra- 
tive of the development of a people. Such a narrative 
is being constantly purified by the elimination of data, 
too credulously accepted, and deepened by the addition 
of new data and new points of view. 

The logician's interest in history concerns the meth- 
ods used to secure the material, the presence of selec- 
tion, analysis and interpretation, the part played by 
guiding-ideas, and the importance of constructive im- 
agination. Modern scientific method in history is a 

1 Whitehead, Introduction to Mathematics, p. 238. 

2 See Langlois and Seignobos, Introduction to the Study of History. 



EXPLANATION AND SYSTEM-FORMATION 291 

monument to the ideal of truth in a complex field in 
which difficulties exist at every step. The historian has 
been forced by his problems into self-consciousness so 
that there are several excellent discussions of historical 
method easily obtainable. Let us look at some of the 
conclusions which bear upon the elements of induction. 

First of all, there have been spirited controversies in 
regard to the purpose of history. There have been po- 
litical historians, moral historians, sociological histori- 
ans ; and, corresponding to these, there have been his- 
torical schools. Upon only one point have all agreed, 
viz., that truth must be the ideal. Within minor diver- 
gencies, a large guiding-idea is now held in common. 
Development is the keynote. " We have noted that the 
scope of history has broadened by taking more and 
more factors into account. Wars and statecraft are now 
regarded as a less important part of national life. This 
has come about not merely through curiosity to find 
out how people lived in time past, but in the search 
after the explanation of national development . . . 
The thread upon which the story of any nation hangs 
is development from the past into the present." 1 His- 
tory seeks to explain, just as any other developed sci- 
ence does, but it explains by development. The com- 
position of causes back of an event or institution is 
always more or less unique. 

The search for documents is a science in itself and 
involves the collaboration of many subordinate sci- 
ences, such as palaeography, epigraphy, and philology. 
But this technique is controlled by the plans and ideas 
of investigators. Given the material, the next step 

1 Vincent, Historical Research, p. 10. 



292 THE ESSENTIALS OF LOGIC 

is the determination of facts. "The document is the 
starting-point, the fact the goal. Between this start- 
ing-point and this goal he has to pass through a com- 
plicated series of inferences, closely interwoven with 
each other, in which there are innumerable chances of 
error; while the least error, whether committed at the 
beginning, middle, or end of the work, may vitiate all 
his conclusions." * The facts of history, in other words, 
are judgments, not observations. 

There are many sources of error of a distinctly men- 
tal character. Sometimes there is reason to doubt the 
good faith of the author. Sympathy often plays its se- 
lective and distorting part ; again, vanity and deference 
to public opinion may be at work. The result of expe- 
rience has been the rise of a defensive canon, called 
4 methodical distrust.' This canon will bring home to 
the student the discussion of some of the causes of error 
in observation given in Chapter XVII. With a char- 
acteristic statement of it we shall close the present dis- 
cussion of scientific systems, for it generalizes that atti- 
tude of reflection and criticism which it is the task of 
logic on its practical side to enforce. " We must not 
postpone doubt till it is forced upon us by conflicting 
statements in documents ; we must begin by doubting." 2 
We must try to secure " that methodically analytical, 
distrustful, not too respectful turn of mind which is 
often mystically called ' the critical sense ' but which is 
nothing else than an unconscious habit of criticism." 3 

1 Lang-lois and Seignobos, Introduction to the Study of History, p. 64. 

2 Ibid., p. 157. 8 Ibid., p. 190. 



EXPLANATION AND SYSTEM-FORMATION 293 

REFERENCES 

Dewey, How We Think, chap. ix. 

Jones, Logic, Inductive and Deductive, pt. in, chaps. I and in. 

Joseph, An Introduction to Logic, chap, xxiii. 

Pillsbury, Essentials of Psychology, chap. ix. 

Poincare', Science and Method, passim. 

Whitehead, Introduction to Mathematics, chap. XVI. 

Langlois and Seignobos, Introduction to the Study of History. 



CHAPTER XXV 

TRUTH AND ITS TESTS 

Back to the Definition of Logic. Logic was de- 
fined as ■ the science of the principles and conditions of 
correct thinking.' This definition was offered as a guide- 
post to direct attention to the general character of the 
subject. Now that we have covered the various topics, 
we must come back to the definition, analyze the terms, 
and permit ourselves to suggest and briefly discuss some 
of the larger and more philosophical problems which 
have all along hovered in the background. What stu- 
dent has not asked himself Pilate's question. If logic 
deals with the conditions and principles of correct think- 
ing, it must contain some standard of correctness. While 
it is not the business of logic to decide what ideas are 
true, — i.e., what the empirical content of truth is, — 
it does seem to be a part of its task to give analytic 
knowledge of the meaning of truth and of the princi- 
ples and methods actually used in testing assertions 
which lay claim to this apotheosis. 

In order to think correctly, we must think both con- 
sistently and truly. Let us look at these two pre- 
requisites for a moment. It is impossible to think truly 
without thinking consistently, but it is possible to think 
consistently without thinking truly. But very few men 
want to think only consistently. The one is a means to 
the other, valued largely because of this relation. 

The Nature of Consistent Thinking. To think 



TRUTH AND ITS TESTS 29,5 

consistently means to avoid self-contradiction. The 
conclusions we draw must be related to the premises we 
accept in accordance with logical necessity. Consistent 
thinking must not sin against the Laws of Thought and 
must contain a recognized harmony among its parts. 
When such thinking is also in agreement with the facts, 
we are apt to speak of it as true and its product as truth 
or valid knowledge. 

We have come to see that clear and well-organized 
ideas are essential conditions of consistent thinking. 
Definition and analysis help to make the ideas we use 
clear and unambiguous, w r hile classification, in which 
concepts are ordered in relations of coordination, sub- 
ordination, and superordination, is another prime con- 
dition of good thinking. Only knowledge which is dis- 
tinct and well organized can be handled without serious 
danger of error. 

Thought discovers internal relations between proposi- 
tions of such a character that one follows from others. 
The sign of such a logical relation is words like ' there- 
fore ' and ' hence.' M is P and S is M; therefore S is 
jP. If we grant the premises, it is impossible to deny 
the conclusion without self-contradiction. If the damp- 
ness of the sidewalk is the sign of either rain or dew, 
this case of dampness signifies that it rained last night 
or that there was a fall of dew. The mind feels itself 
forced to draw the conclusion, once it has admitted a 
general rule and recognized a specific instance as com- 
ing under the rule. Such logical necessity is, in a sense, 
the inverse of the act of generalization. Were we un- 
able to generalize, we should be unable to infer, and the 
word, therefore, would have no meaning for us. This 



296 THE ESSENTIALS OF LOGIC 

fact reveals the intimate relation of induction and de- 
duction. 

The Laws of Thought. We have postponed the 
treatment of the traditional Laws or Axioms of Thought, 
because they are apt to appear trivial and meaningless 
when taken up at the beginning without a logical context. 
These primary axioms of thought are three in number 
and state the recognized conditions of consistent think- 
ing. So far as I can see, they arise from and express 
the very nature of conceptual thinking. For that rea- 
son, however, they are as self-evident as the axioms of 
Euclidian geometry. After formulating them, I shall 
try to relate them to the act of thinking. 

The Laws of Thought are : — 

(1) The Law of Identity. A is A. 

(2) The Law of Contradiction. A is not not- J.. 

(3) The Law of Excluded Middle. Everything is 
either A or not- A. 

It is obvious that these axioms need some interpreta- 
tion in order to give meaning to the symbolic form in 
which they are stated. We shall start with the Law of 
Identity, develop its meaning, and then show that the 
other laws are simply further explications of it in the 
light of the negative. 

The Law of Identity carries us back to the nature of 
concepts. A concept is a mental object which we can 
hold before the attention, think about, and distinguish 
from other objects. But before this can be done, these 
mental objects must have a certain degree of stability 
and distinctness of content. Hazy, vague, uncertain 
thoughts are condemned by logic because they are not 
full-fledged ideas. We all know when we have such im- 



TRUTH AND ITS TESTS 297 

mature concepts before our minds — at least, we do 
when we are reflective and have learned to distinguish 
between concepts and words. Since one of the princi- 
ples of logic is non-ambiguity, one of its ideals must be 
clear and distinct concepts. Now, such clear and dis- 
tinct concepts are recognizable and distinguishable from 
others. It is this fact that the Law of Identity points 
out. No thought and no judgment is possible where 
concepts cannot be held before the mind, retained, re- 
produced, and recognized as the same. This sense of 
sameness is, as James phrased it, " the very keel and 
backbone of thinking.'' 

The Law of Contradiction is the negative side of the 
Law of Identity. If we are able to present clear ideas 
to the mind, we must also be able to distinguish them 
from one another. To apprehend A is also to know that 
it is not not-^L 

There is another form of the Law of Contradiction 
which concerns itself with judgment rather than with 
the character of concepts. This other form is usually 
called the Aristotelian and is as follows : " It is impos- 
sible that the same predicate can both belong, and not be- 
long, to the same subject, at the same time, and in the 
same sense." This formulation brings out sharply the na- 
ture and meaning of contradiction by calling attention 
to the fact that the human mind cannot accept the judg- 
ments 4 A is BJ and ' A is not B ' at the same time. 

The Law of Excluded Middle is a further definition 
of the relation between a term and its contradictory. 
It asserts that of two contradictory assertions one is 
necessarily true. There can be no third possibility. In 
formal logic, this principle appears in the fact that 



298 THE ESSENTIALS OF LOGIC 

there are only two qualities^ the affirmative and the 
negative. 

The Postulates of Logic. Besides these axioms, 
certain postulates are sometimes advanced as essential 
to logic. The following is a partial list : (1) Every as- 
sertion is either true or false. (2) Some propositions 
may be recognized as true. (3) The mind is able to 
apprehend objects. (4) There are universal connections 
in nature, and some at least of these can be discovered. 

(5) The world is essentially the same for all observers. 

(6) Individuals who communicate can mean essentially 
the same by their terms. The investigation of these 
postulates is usually assigned to epistemology and 
metaphysics. 

The Question of Truth. Consistency with other 
propositions is not by itself a sufficient criterion of 
truth. An assertion may follow with due logical neces- 
sity from temporarily accepted premises, but such an 
internal relation cannot guarantee the system as a whole. 
While the accepted premises justify the conclusion, 
they themselves must be justified. But does not this 
situation lead us into a difficulty ? Can we have any- 
thing more than consistency? Suppose that we use the 
term 6 valid ' for a conclusion which follows from ac- 
cepted premises with logical necessity. The question 
which confronts us is this, Can we attain anything but 
valid assertions ? But, if this be the case, our ultimate 
premises must either be given with their credentials by 
some sort of extra-logical intuition, or must be accepted 
on authority, or, finally, be postulated. Is there any 
way to avoid this unwelcome series of disjunctions ? 

I hope that the student has seen that this way of 



TRUTH AND ITS TESTS 299 

approach to the question of truth has stressed the de- 
ductive side of logic to the exclusion of induction. 
Were thinking only deductive, we should be compelled 
to face the unwelcome alternatives outlined above. It 
has been the prime fallacy of many of the philosophical 
systems of the past to seek some one principle from 
which to deduce reality as experienced. In my opinion, 
such an attempt is illogical because it exalts deduction 
over induction and does not see that knowledge is a 
growth in which both aspects, or phases, of thinking are 
at work. 

'Validity' is, then, essentially a deductive term 
while 4 truth ' corresponds more to that intimate inter- 
play of induction and deduction which has been pre- 
sented in our study of science. It will be remembered 
that there are three elements, or distinguishable mental 
processes in all systematic investigation, namely, the 
inductive element par excellence, whose principle is ob- 
servation with its fidelity to fact ; the generalizing and 
hypothesis-forming element ; and, lastly, deductive rea- 
soning out of implications. These elements are inter- 
twined according to the exigencies of the case. It is 
out of the inductive-deductive interaction of fact and 
theory that truth, as distinct from mere validity, arises. 

The Criteria of Truth. It has been customary to 
speak of truth and to contrast it with error. This col- 
lective way of speaking about truth as a body of doc- 
trine has too often led people to think of truth in a 
mystical fashion. Even critical thinkers have com- 
mitted the ' fallacy of abstract terms,' 1 and thought of 
truth as an abstract entity. In order to avoid this dan- 

1 See chapter in. 



300 THE ESSENTIALS OF LOGIC 

ger, it is best to distinguish between true ideas and 
false ideas. And, by ideas, we shall mean assertions, 
propositions, judgments, theories, in fact all mental 
objects in regard to which we make the truth-claim. 
Our present purpose is to discover the actual, empirical 
tests which are used in investigation to decide between 
ideas which tentatively claim truth and yet conflict. 
What are the criteria of true ideas ? And what is the 
logical setting of these criteria f 

Reviewing our study of systematic investigation, we 
note that investigation is begun only when some prob- 
lem arises. Every such problem must have a concrete 
and specific character. In truth, the scientist is well 
aware that his first task is to define his problem, for any 
lack of clearness in the statement of the problem is cer- 
tain to thwart his efforts. To work on an ill-defined 
problem is like hunting for something of which one 
has no clear picture. The next step is the separation of 
what is certain from what is uncertain. He wants to 
know what he can depend on, what is beyond question 
for the purpose in hand. The logician calls the certain- 
ties of the field relevant to the specific problem the 
4 data,' and contrasts the conjectures and hypotheses, 
which arise in the fertile mind of the scientist, with 
these data as 'theory.' It must be remembered that 
such theories develop in the mind of the expert who 
has detailed familiarity with what has been discovered 
and achieved in this particular field and in those ad- 
joining. An hypothesis is not external to the knowledge 
of the field but is a genuine branch of it. The tree of 
human knowledge is vigorous and puts forth many 
shoots, some of which must be lopped off. The process 



TRUTH AND ITS TESTS 301 

of selecting among competing explanations by marking 
their capacity to cover and organize the facts and so 
solve the specific problem is called verification. Veri- 
fication involves responsibility to fact, freedom from 
self-contradiction, and a flexible harmony with other 
accepted theories which have passed through the same 
test. In any particular case, such testing is a complex 
process in which the mind works back and forth be- 
tween data and theory, adding new data and modifying 
the theory. The criteria of truth are not external but 
internal. It is absurd to look for some touchstone which 
can be applied in a mechanical fashion to propositions 
claiming truth. 

Degrees of Belief. Assertions are not made with 
the same degree of assurance, nor, to state the same fact 
in more psychological language, is there only one degree 
of belief. The traditional logic was accustomed to rec- 
ognize this fact in its theory of modals. i The earth re- 
volves around the sun ' is an assertoric judgment. A 
dictum is asserted flatly. ' It may rain this afternoon f 
is a problematic judgment. In science, the stage of 
conjecture represents the problematic mode. ' Gravita- 
tion may be explained in terms of electricity,' 6 Mass 
may turn out to be a dynamic effect of something more 
ultimate,' are examples. An apodeictic judgment, on the 
other hand, expresses a sense of logical necessity. The 
grounds for the judgment are given or intimated. 
4 There must be a presidential election this year ' is apo- 
deictic. The ground intimated is, of course, the federal 
law on the subject. 

Modality reflects the fact that ideas have different 
settings. Beliefs are held with more or less faith. The 



302 THE ESSENTIALS OF LOGIC 

upper limit of belief is dogmatic certainty, while the 
other extreme is a low degree of probability. The logi- 
cian encourages individuals to give up dogmatic cer- 
tainty and to make practical certainty the highest de- 
gree of belief. There is a continuous shading of belief 
from mere probability, in which the evidence is weak, 
to practical certainty in which there is no longer any 
factually motivated doubt. Rational belief is belief 
founded on grounds, and such grounds must ultimately 
come back to critically tested fact. 

What the Attainment of True Ideas implies. 
There are at least four things implied in the attain- 
ment of true ideas : (1) the ability to obtain facts (ob- 
servations, testimony, evidence) ; (2) the right to 
make use of past experience which is not challenged by 
reasonable doubt ; (3) the Principle of Universal Con- 
nections, the Uniformity of Nature, the Law of Uni- 
versal Causation ; (4) the mental capacity for analysis, 
conjecture, construction, and deductive reasoning. 

These four things are largely self-explanatory when 
taken in the light of what has already been said about 
them in the preceding chapters. Unless we could obtain 
facts, which are assertions about which there is no 
motivated doubt, it would be impossible to generalize, 
to form hypotheses, or to verify by the convergence of 
evidence. Unless past knowledge were applicable, it 
would be impossible to have guidance in an attack on 
new problems or to determine what was relevant and 
what irrelevant ; again, it would be impossible to build 
up systems of knowledge such as are found in the vari- 
ous sciences as well as in practical life. Knowledge is, 
as we have so often pointed out, a growth. While the 



TRUTH AND ITS TESTS 303 

old may be modified by the new facts and theories, it 
yet remains as something substantial within which to 
work. That universal connections exist and can be dis- 
covered is a postulate which underlies all scientific in- 
vestigation. It cannot be proved in any demonstrative 
way, but is suggested and in a way verified by expe- 
rience. Finally, logic assumes that the mental capaci- 
ties which human beings possess, working upon the ma- 
terial given by observation and testimony, are able to 
achieve ideas which give genuine knowledge. To doubt 
this ability to attain knowledge is for logic an ultimate 
scepticism which it refuses to acknowledge. Both our 
practical and our intellectual instincts revolt against the 
suggestion that what we take to be knowledge is not 
knowledge. 

The Meaning of Truth. Having given the empiri- 
cal criteria of ; truth ' and their logical setting, let us 
be bold enough to discuss the meaning of this term. 
What do we mean by ' true ' ideas ? How do such 
ideas differ from ' false ' ideas ? Controversial battles 
have been waged in philosophy over the meaning of 
these terms. Into the details of such controversies, it 
is not here the place to enter. We must be brief and 
clear, and trust that the position adopted will commend 
itself to the reason of those who have carefully studied 
the preceding pages. 

Let us admit the hazard that what we take to be 
true may not be true. The problem still remains that 
we mean something by this term. An idea is true which 
meets the empirical criteria and which tve therefore 
take to be a case of knowledge. An idea is true which 
has stood the test of motivated doubt, has come out 



304 THE ESSENTIALS OF LOGIC 

victorious, and, due to that fact, is accepted by the 
mind as fulfilling its claim to be an idea of, or about, 
something. It is the very nature of an idea to claim to 
give knowledge. When this claim is granted by the 
mind, the idea is accredited or accepted as genuine 
knowledge ; and the term true is used to express this 
attitude of approval. Thus, it is a contrast term with 
4 false ' as its counterpart. Just as actions are quali- 
fied as right or wrong, so ideas — i.e., judgments, pro- 
positions, assertions — are qualified as true or false. 
This latter qualification gets its meaning, however, from 
the claim to be cases of knowledge which it is the very 
nature of such judgments to assert. 

There can be little doubt that the methods by which 
ideas are tested enter into the meaning of truth to a 
greater or lesser extent. What is called 4 pragmatism' 
is a stimulating but, I believe, one-sided emphasis on this 
aspect of the meaning of truth. " True ideas" writes 
James, " are those that we can assimilate, validate, 
corroborate and verify. False ideas are those that we 
cannot. That is the practical difference it makes to us 
to have true ideas ; that, therefore, is the meaning of 
truth, for it is all that truth is known-as." l It will be 
noticed that the meaning of being an actual case of 
knowledge, which is a part of the content and setting of 
every assertion, is omitted. This aspect is, in our opin- 
ion, fundamental. The logician who understands his 
science does not deny the empirical character of the 
criteria of trueness, but he does assert that the claim 
of an idea to be knowledge is also essential. " Knowl- 
edge is an achievement and possession of minds as these 

1 James, Pragmatism, p. 201. 



TRUTH AND ITS TESTS 305 

have evolved under the stimulus of their environment. 
As a meaning, knowledge precedes truth, which is a 
reflective deepening of the sense of knowledge in the 
light of an awakened doubt. The criteria of truth are, 
therefore, the same as those of knowledge. Thus truth 
is accepted and tested knowledge. To say that an idea 
is true is to say that it is actually a case of knowledge 
as it claims to be. Truth is knowledge triumphant in- 
stead of knowledge militant ; yet it is knowledge, as 
can be seen when we combine the two terms and speak 
of true knowledge." x 

Truth and the Will to believe. Of recent years 
there have been several stimulating essays on the rela- 
tion of will and our passional nature in general to be- 
lief. By consensus of opinion, the two most striking of 
these are James's The Will to Believe and Clifford's 
The Ethics of Belief These two writers hold positions 
which are different both in their tenor and in their con- 
clusions. It will repay us to examine their discussions 
of the foundations of belief for this will introduce us 
to the larger setting of logic. 

Let us begin with The Will to Believe. As a psy- 
chologist, James rightly first considers the actual psy- 
chology of human opinion. " When we look at certain 
facts, it seems as if our passional and volitional nature 
lay at the root of all our convictions. When we look 
at others, it seems as if they could do nothing when the 
intellect had once said its say." 2 Taking up the latter 
facts first, he writes : " Does it not seem preposterous 

1 Sellars, Critical Realism, p. 282. 

2 James, The Will to Believe; page references are to Representative 
Essays in Modern Thought, 



306 THE ESSENTIALS OF LOGIC 

on the very face of it to talk of our opinions being 
modifiable at will? Can we, by just willing it, believe 
that Abraham Lincoln's existence is a myth, and that 
the portraits of him in Mc duress Magazine are all of 
some one else? . . . We can say any of these things, 
but we are absolutely impotent to believe them ; and 
of just such things is the whole fabric of the truths 
that we do believe in made up, — matters of fact, im- 
mediate or remote, as Hume said, and relations between 
ideas, which are either there or not there for us if we 
see them so, and which if not there cannot be put there 
by any action of our own" (p. 76). I feel that it is 
best to quote this side of James's teaching quite fully, 
since justice has not been done to it. James permits 
the 'will to believe' only in certain fields and under 
certain circumstances. " The talk of believing by our 
volition seems, then, from one point of view, simply 
silly. From another point of view it is worse than silly ; 
it is vile. When one turns to the magnificent edifice of 
the physical sciences, and sees how it was reared ; what 
thousands of disinterested moral lives of men lie buried 
in its mere foundations ; what patience and postpone- 
ment, what choking down of preference, what submis- 
sion to the icy laws of outer fact are wrought into its 
very stones and mortar ; how absolutely impersonal it 
stands in its vast augustness, — then how besotted 
and contemptible seems every little sentimentalist who 
comes blowing his voluntary smoke wreaths, and pre- 
tending to decide things from out of his private dream " 
(p. 78). 

But, as James points out, there is an interaction be- 
tween our knowledge, our values, our aspirations, and 



TRUTH AND ITS TESTS 307 

our prejudices. The mind is an organic whole, and it 
is impossible to find an intellect separate from the 
movement of experience. Facts and theories are not 
independent, for their discovery, selection, relative im- 
portance and control, of the outlook of the individual ; 
and this outlook is a synthesis of ideas and feelings. 
That this is the case we have tried to bring out in the 
study of induction. But the logician urges the individ- 
ual to allow the outlook to be more a function of in- 
vestigation, to make the factual side the control-side. 
The logician sets an ideal which he admits is seldom 
approached. This control of outlook by ' fact ' is the 
aim which lies back of the inductive principle of fidelity 
to fact and the internal criteria of truth, the conver- 
gence of relevant evidence. Thus logic stresses the 
avoidance of error, on the one hand, and the positive 
methods of attaining new truth on the other. Its aim 
is to make the individual critically reflective toward 
assertions and beliefs. 

Let us now turn to the thesis which James defends : 
" Our passional nature not only lawfully may, but 
must, decide an option between propositions, whenever 
it is a genuine option that cannot by its nature be de- 
cided cm intellectual grounds ; for to say, under such 
circumstances, 4 Do not decide, but leave the question 
open,' is itself a passional decision, — just like decid- 
ing yes or no — and is attended with the same risk of 
losing the truth" What strikes the logician in this 
thesis is the assumption that there are problems " which 
by their very nature cannot be decided on intellectual 
grounds " (p. 81). It is this assumption that the logician 
cannot admit if by intellectual grounds are meant factual 



308 THE ESSENTIALS OF LOGIC 

grounds. Such problems could not be formulated and 
defined. 

But James at least suggests that other problems than 
non-rational ones are also to be treated by our passional 
nature. And here there is an ambiguity in his treat- 
ment. As against Clifford, he insists that we do not 
need to shut our eyes to a possibility of belief just be- 
cause the problem has not been settled and there is also 
a possibility of error. With this I agree. There are 
degrees of belief ; and, when evidence can be advanced 
both for and against a position, neither affirmation nor 
negation should be dogmatic. I can understand why 
such a temperament as James's rebelled against the stoi- 
cism of Clough, Huxley, and Clifford which sang: — 

It fortifies my soul to know- 
That, though I perish, Truth is so. 

When there is probability only, probability is by its 
very nature both for and against. The probability of 
throwing a six-spot is one sixth and the chances against 
are five sixths. James has the right to stress the prob- 
ability for, while Clifford has an equal right to stress 
the negative side, the motivated doubt. 

But there runs through James the suggestion of an- 
other test of truth than that worked out by science and 
logic. It is not prominent, but it is present enough to 
have led many to interpret his position in accordance 
with it. This second standard consists in an appeal to 
personal feelings and satisfactions as a foundation 
for truth. Such feelings are facts, but they are not 
the only facts, nor are they the least changing and com- 
mon of facts. To make them the dominant criteria is, 
therefore, to forsake an objective and thorough inves- 



TRUTH AND ITS TESTS 309 

tigation in favor of what experience has proved to be 
personal and incomplete. 

The Logic of Doubt. In contrast to the essay by 
James, Clifford's treatment savors almost of a justifica- 
tion of doubt. And, from the logician's standpoint, 
much can be said in favor of such an attitude. Belief, 
as a rule, takes care of itself, while doubt and open- 
mindedness are trained habits not easily acquired. Clif- 
ford stresses what may be called the i ethical aspect ' 
of logic ; and in his attitude there is much that reminds 
us of the Puritan and the Stoic. James was a brilliant, 
tender-minded, broad-minded mystic; Clifford was a 
rigorous, tough-minded, intellectual idealist. 

" A shipowner was about to send to sea an emigrant 
ship. He knew that she was old, and not overwell 
built at the first ; that she had seen many seas and 
climes, and often had needed repairs. Doubts had been 
suggested to him that possibly she was not seaworthy. 
These doubts preyed upon his mind, and made him un- 
happy ; he thought that perhaps he ought to have her 
thoroughly overhauled and refitted, even though this 
should put him to great expense. Before the ship 
sailed, however, he had succeeded in overcoming these 
melancholy reflections. . . . He would dismiss from 
his mind all ungenerous suspicions about the honesty 
of builders and contractors. In such ways he acquired 
a sincere and comfortable conviction that his vessel 
was thoroughly safe and seaworthy . . . ; and he got 
his insurance money when she went down in midocean 
and told no tales. 

" What shall we say of him ? Surely this, that he 
was verily guilty of the death of those men. It is ad- 



310 THE ESSENTIALS OF LOGIC 

mitted that he did sincerely believe in the soundness of 
his ship; but the sincerity of his conviction can in no 
wise help him, because he had no right to believe on 
such evidence as teas before him. He had acquired his 
belief not by honestly earning it in patient investiga- 
tion, but by stifling his doubts." 1 

Clifford's conclusion is : " It is wrong always, every- 
where, and for any one, to believe anything upon insuf- 
ficient evidence" (p. 54). " 'But,' says one, *I am a 
busy man ; I have no time for the long course of study 
which would be necessary to make me in any degree a 
competent judge of certain questions, or even able to 
understand the nature of the arguments.' Then he 
should have no time to believe" (p. 54). It must have 
been this last pronouncement which made James call 
him " that delicious enfant terrible" Let us soften it 
somewhat by saying that he should have no time for 
dogmatic belief, for that belief which shuts out evi- 
dence when it comes and passes harshly and uncom- 
promisingly into action. 

REFERENCES 

Bode, An Outline of Logic, chap. XV. 

James, The Will to Believe and other Essays in Popular Philos- 
ophy. 

James, Pragmatism, chap. VT. 

Clifford, The Ethics of Belief . 

Gibson, The Problem of Logic, chaps. I and in. 

Sellars, Critical Realism, chap. X. 

1 Clifford, The Ethics of Belief, Bepresentative Essays, pp. 46-47. 



QUESTIONS AND EXERCISES 

CHAPTER I 

1. Analyze the definition of logic given, and compare it 
with definitions to be found in other texts. 

2. Distinguish between a theoretical and an applied sci- 
ence. Give examples of both. 

3. What is meant by 'utilitarian' when the term is used in 
its narrower sense? 

4. Point out and explain why logic has a practical value in 
education. 

5. Name the various kinds of logic. Why have these 
developed? 

6. With what other sciences is logic related? 

7. How does the purpose of logic differ from that of rhetoric? 

8. To what extent do logic and psychology have the same 
subject-matter ? 

9. Where does logic find its material? Why is introspec- 
tion alone not sufficient? 

10. Recall an actual case of reasoning and try to analyze it. 

CHAPTER II 

1. State some of the mental processes to which the term 
'thinking' is applied. Give examples to bring out dif- 
ferent levels of thinking. 

2. Distinguish between 'imagination,' 'memory,' and 'rea- 
soning.' Make two illustrations of each. 

3. What are some of the social conditions of thought? Name 
some of the great periods in history distinguished by 
mental boldness and energy. 

4. Can you name any great men who owed much to some 
stimulus which awakened their mental curiosity? 

5. "Thinking arises out of the need for adjustment." 
Explain. 

6. What processes are preliminary to reasoning? Distin- 
guish between 'perception' and 'conception.' 



SU QUESTIONS AND EXERCISES 

7. Collect five statements which you would call * facts.' 
Can you find any element of inference or theory in them? 

8. Take any field in which you are especially interested, 
and show that your insight has increased with further 
study. 

9. Give at least four cases where your perception of a thing 
or of an event has been changed by further knowledge. 

10. Do you think that the public schools in America stimu- 
late genuine thinking as much as is desirable? Be pre- 
pared to support your opinion. 

CHAPTER III 

1. Distinguish between a 'logical term' and a 'word/ 

2. In the following list, point out which terms are concrete 
and which are abstract: — 

virtue education solitude life 

American democracy asparagus time will 

detachment consciousness auto cavalry 

iron man paper fate 

3. Make a list of five examples of collective terms. 

4. Distinguish between general and singular terms. Make 
a list of five of each kind. 

5. Do you think that the distinction between singular and 
general can be applied to abstract terms? 

6. Explain the fallacy of hypostatization. Give three 
examples which show at least an approach to this 
fallacy. 

7. What are relative terms? Give five examples. 

8. Explain the danger in discussions about 'poverty,' 
'educational progress,' 'the growth of democracy.' 

9. Distinguish between positive and negative terms. Give 
three examples of each. Is the form always an index to 
the meaning? 

10. Explain the distinction between 'denotation' and 'con- 
notation.' 

11. Make a series of at least six terms arranged in order of 
increasing denotation. Arrange the same terms in order 
of increasing connotation. 

12. Show that terms which do not have any connotation 
still have meaning. 



QUESTIONS AND EXERCISES 313 

CHAPTER IV 

1. Why is language such an important condition of think- 
ing? 

2. State the logical law of language. 

3. What are some of the causes of ambiguity? 

4. Give ten examples of univocal words. Are technical 
terms always univocal? 

5. In the following exercises select those terms of which 
the meaning is most uncertain. State and justify the 
meaning which you think belongs to the term in its 
present context: — 

(1) We should live according to Nature. 

(2) All men have natural rights. 

(3) America is a democratic country. 

(4) International law must be binding on all peoples. 

6. Make a list of five words which have decidedly changed 
their meaning during the last hundred years. 

7. Distinguish between vagueness and ambiguity. Show 
why abstract terms are peculiarly liable to vagueness. 

8. Try to formulate the divergent notions of * force,' ' mat- 
ter,' and ' motion ' that are expressed or implied in the 
following extracts from Buechner's Force and Matter: — 

"No force without matter — no matter without 
force. One is no more possible, and no more imagin- 
able by itself than the other. . . . Force and matter 
are fundamentally the same thing, contemplated 
from different standpoints. In the material world 
we know of no example of a particle of matter not 
endowed with force or working by it. We must further 
admit on closer investigation, that matter as such 
could make no impression on our sense-organs or 
minds; it can only do this by means of the forces 
united with or at work within it. A piece of lead held 
in the hand presses on it because of the attractive 
force of the earth and so produces the idea of weight. 
. . . Nothing can prove to us the real existence of a 
force, except the properties, changes and movements, 
which we become conscious of in matter, and these 
we call different 'forces' according to the resemblances 
or differences in such manifestations; any knowledge 



314 QUESTIONS AND EXERCISES 

of them by other ways is impossible. . . . Force may 
be defined as a condition of activity or a motion of 
matter or of the minutest particles of matter or a 
capacity thereof; yet more precisely, as an expression 
for the reason of a possible or actual movement. . . . 

"Motion must be regarded as an eternal and insepa- 
rable property or as a necessary condition of matter. 
Matter without motion exists no more than matter 
without force; motion without matter exists as little 
as force without matter. Nor can motion be deduced 
from any force, for it is the very essence of force it- 
self, and can therefore have no origin, but must be in 
all places. . . . The most solid body owes its condi- 
tion only to the mutual attractive force of its minutest 
particles, which continually oscillate or swing round 
the so-called center of gravity, and without which it 
would at once fall to pieces. That these particles are 
never able to attain a condition of relative rest is 
proved by the universally present force of heat, which 
is known to be nothing more than a mode of motion 
and which, since all bodies without exception contain 
heat, keep these smallest particles or molecules in a 
state of continual movement. . . . Motion must there- 
fore be regarded as the primal condition or in some 
measure as the soul of matter." l 

CHAPTER V 

1. What is classification? Out of what need does it arise? 

2. Distinguish between 'artificial' and 'natural* classi- 
fications. 

3. How has the theory of evolution affected scientific 
classification? 

4. What is a 'dichotomous' division? Under what condi- 
tions might it be advantageous? 

5. Criticize the following divisions : — 

(1) Religions, into Christian, Mohammedan, and 
non-Christian. 

(2) Pictures, into paintings, engravings, posters, and 
pen-and-ink sketches. 

1 Quoted from Bode. An Outline of Logic. 



QUESTIONS AND EXERCISES 315 

(3) Schools, into technical, vocational, and public. 

(4) Furniture, into Colonial, Sheraton, Adams, office, 
and home. 

(5) Political parties, into Republican, Radical, and 
Conservative. 

6. Divide and subdivide the following : — 

Governments, Sciences, Sports, Schools. 

7. State and explain the technical terms used in division. 

8. What part does purpose play in both classification and 
division? 

CHAPTER VI 

1. Why is definition needed? 

2. Show the relation between ' definition' and 'classifica- 
tion.' 

3. Define the following terms by proximate genus and es- 
sential difference : — 

Democracy, Education, Tariff, Politics, American, 
Honor, Wealth, Neutrality. 

4. Examine the following definitions to see whether they 
conform to the logical rules of definition: — 

(1) The body is the emblem or visible garment of the 
soul. 

(2) Life is a continuous adjustment of internal to ex- 
ternal relations. 

(3) A phonograph is a mechanism for recording and 
reproducing sounds. 

(4) Life is the opposite of death. 

(5) Psychology is the science of the processes whereby 
an individual becomes aware of a world of objects 
and adjusts his actions accordingly. 1 

(6) Psychology is the science of the phenomena of 
consciousness. 2 

(7) Education is the eternal process of superior ad- 
justment of the physically and mentally developed, 
free, conscious human being to God, as mani- 
fested in the intellectual, emotional, and volitional 
environment of man. 3 

(8) Education is conscious or voluntary evolution. 4 

1 Stout. 2 Baldwin. 3 Home. * Davidson. 



316 QUESTIONS AND EXERCISES 

(9) Religion consists in the feeling of absolute de- 
pendence. 1 

(10) Religion is a desire manifested by prayer, sacri- 
fice, and faith. 2 

(11) Religion is a faculty of the mind by which, inde- 
pendently of the senses and of reason, man is able 
to perceive the Infinite. 3 

5. Show that a definition is always relative to the purpose 
entertained. 

6. What are the predicables? Distinguish between a 'dif- 
ferentia' and an 'accident.' 

7. Write out a list of at least five words or phrases which 
you regard as catch-words which need definition. 

8. Look up the platforms of the various political parties for 
words which seem to you to need definition. 

CHAPTER VII 

1. Distinguish between 'assertions' and 'propositions.' 
What was the error of the more formal logic of the past? 

2. Show that judgment is a process of interpretation end- 
ing in an assertion. 

3. Bring out by at least three examples the genetic side of 
judgment. 

4. Show that the world as we experience it is a product of 
past mental activity. 

5. In what sense are there levels of judgment? Give cases 
to prove the increasing complexity of judgment as we 
pass from concrete things to principles. 

6. What two aspects are there to every judgment? 

7. Distinguish between the actual operation of judging and 
its verbal expression. What is the purpose which con- 
trols language? 

8. What is meant by the 'universe of discourse'? Indicate 
the reason for its importance in the proper interpretation 
of propositions. 

1 Schleiermacher. 2 Feuerbach. 8 Max Mtiller. 



QUESTIONS AND EXERCISES 317 

CHAPTER VIII 

1. Distinguish between 'categorical/ 'hypothetical,' and 
'disjunctive' propositions. 

2. What is meant by the 'quantity' of propositions? By 
their 'quality'? 

3. Throw the following propositions into logical form, 
give the letter that symbolizes the quantity and quality, 
and state the distribution of the terms: — 

(1) Not all who are called are chosen. 

(2) Few were saved. 

(3) None of the planets except the earth is inhabited. 

(4) He can't be wrong whose life is in the right. 

(5) More haste less speed. 

(6) All politicians are not dishonest. 

(7) Only noble deeds deserve praise. 

(8) Mercy but murders, pardoning those that kill. 

(9) No one is always happy. 

(10) Only some citizens have the right to vote. 

4. Explain why negative propositions always distribute the 
predicate. 

5. Apply the graphical method to the four kinds of cate- 
gorical propositions. 

6. What is the purpose underlying the logical manipulation 
of propositions. 

CHAPTER IX 

1. What is immediate inference? 

2. Be prepared to write down and explain the Square of 
Opposition. 

3. What propositions are true, false, or doubtful', — 

(1) when A is false; (3) when I is false; 

(2) when E is false; (4) when is false? 

4. What is the simplest proposition which must be estab- 
lished in order to disprove the following statements: — 

(1) All men desire wealth. 

(2) No man is perfectly happy. 

(3) Some knowledge is not of any value. 

(4) Pain alone is evil. 

(5) All is not lost. 1 

1 Creighton. 



318 QUESTIONS AND EXERCISES 

5. Give the converse, the obverse, and the contrapositive 
of each of the following propositions : — 

(1) Only a fanatic believes in panaceas. 

(2) Uneasy lies the head that wears a crown. 

(3) No men are always happy. 

(4) Most of the nations were unprepared. 

(5) None but the industrious deserve to succeed. 

(6) All men are mortal. 

(7) Discontent is frequently a symptom of inefficiency. 

(8) Children are noisy on rainy days. 

6. By what process do we pass from each of the following 
propositions to the next? 

(1) No knowledge is useless. 

(2) No useless thing is knowledge. 

(3) All knowledge is not useless. 

(4) All knowledge is useful. 

(5) What is not useful is not knowledge. 

(6) What is useless is not knowledge. 

(7) No knowledge is useless. 1 

7. Test the following arguments by obversion and con- 
version: — 

(1) When we hear that all the righteous people are 
happy, it is hard to avoid exclaiming, What! are 
all the unhappy persons we see to be thought un- 
righteous? 

(2) If a man who has been accustomed to enjoy lib- 
erty cannot be happy in the condition of a slave, 
does it follow that a man who has not been accus- 
tomed to liberty can be happy as a slave? 

CHAPTER X 

1. How did Aristotle define the syllogism? What was the 
germ of his invention? 

2. What is the Dictum de omni et nullo ? 

3. Be prepared to demonstrate each of the rules of the 
syllogism. 

4. What criticism would you be inclined to pass upon the 
syllogism when treated very formally? 

5. Select and name the various propositions and terms of 

1 Jevons. 



QUESTIONS AND EXERCISES 319 

the syllogism in the following informally stated argu- 
ments. Then reconstruct them so as to make formally 
correct syllogisms : — 

(1) All leeches must be true worms; for all annelids 
are worms, and leeches are annelids. 

(2) Caterpillars have true legs; worms do not; and so 
caterpillars are not worms. 

(3) Amphibians are not reptiles, since they breathe 
by gills in the larval stage, and reptiles do not. 1 

6. If either premise of a syllogism is 0, what must the other 
be? 

7. Prove that there must be in the premises one more dis- 
tributed term than in the conclusion. 

8. Prove that if one, but only one, premise is negative, and 
both premises are universal, they will between them dis- 
tribute three terms. 

9. Put the following argument into syllogistic form: — 

How can any one maintain that pain is always an evil, 
who admits that remorse involves pain, and yet may 
sometimes be a real good? 

CHAPTER XI 

1. Arrange the following arguments in logical order. Name 
the figure of the syllogism, and if the argument is in- 
valid, state the formal fallacy involved: — 

(1) All M is P; no M is S; therefore no S is P. 

(2) No P is M; some S is M; therefore some S is 
not P. 

(3) Some useful metals are becoming rarer; iron is a 
useful metal, and is therefore becoming rarer. 

(4) None but whites are civilized; the ancient Ger- 
mans were white; therefore they were civilized. 

(5) Since the virtuous alone are happy, he must be 
virtuous if he is happy, and he must be happy if 
he is virtuous. 

(6) It is not true that a man cannot do a great work 
without a strong physique; for the philosopher 
Kant did a great work and his physique was any- 
thing but strong. 

i Taylor. 



320 QUESTIONS AND EXERCISES 

(7) Only animals are sentient beings; fishes are ani- 
mals; therefore fishes are sentient beings. 

(8) Good men write good books; this is a good book; 
therefore its writer was a good man. 

(9) Every book is liable to error; every book is a hu- 
man production; therefore all human productions 
are liable to error. 

2. Write out the sixty-four moods of the syllogism and 
strike out the fifty-three invalid ones. 

3. Prepare to prove the special canons of each of the four 
figures. 

4. Make a syllogism in E I 0, any figure, and exhibit the 
conversions necessary to accommodate it to each of the 
other figures. 1 

5. Why is the first figure usually considered the standard 
figure? 

6. Supply premises for the following conclusions: — 

(1) Some politicians are not dishonest. 

(2) The moon tends to fall to the earth. 

(3) Banks sometimes fail. 

(4) Some logicians are not good reasoners. 

CHAPTER XII 

1. Complete the following arguments, determine their 
mood and figure, and decide whether they are valid: — 

(1) Blessed are the meek, for they shall inherit the 
earth. 

(2) Only the good are fit to die, therefore capital pun- 
ishment is wrong. 

(3) Let us meet her. Why? They say she's mad. 

(4) Because thou art virtuous, shall there be no more 
cakes and ale? 

(5) None but material bodies gravitate; therefore air 
is a material body. 

2. Construct an enthymeme of each of the three orders. 

3. Construct a complex argument containing a prosyl- 
logism and an episyllogism. 

4. Show why all the premises except the first must be uni- 
versal in an Aristotelian Sorites. 

i Taylor. 



QUESTIONS AND EXERCISES 321 

5. Prove by graphical methods that in the Goclenian So- 
rites the first premise alone can be negative, and the 
last alone particular. 

6. What is an extra-syllogistic argument? Contrast it with 
syllogistic inference. 

7. Why are fallacies more apt to exist in condensed argu- 
ments than in expansed ones? 

CHAPTER XIII 

1. Determine which of the following give valid conclusions 
and which do not; in case of invalidity, name the fallacy: 

(1) If the door were locked, the horse would not be 
stolen; but the horse is not stolen, therefore the 
door must have been locked. 

(2) If all men were capable of perfection, some would 
have attained it; but none having done so, none 
are capable of it. 

(3) If every ghost story is to be believed, we must 
accept the general standpoint of the spiritualists; 
but we cannot accept their general standpoint; 
therefore we cannot believe ghost stories. 1 

(4) 'If he has not studied, he will fail in the examina- 
tion.' With this proposition as a major premise, 
what can be inferred if we take as minor premise : — 

(1) He has not studied. 

(2) He will fail. 

(3) He will not fail. 

(4) He has studied. 

(5) If it becomes colder to-night, there will be a frost; 
but it will not become colder to-night; therefore 
there will be no frost. 

2. Does the categorical or the hypothetical syllogism seem to 
you the simpler? Which of the two stresses denotation? 

3. Where is the source of danger in the disjunctive syllo- 
gism? 

4. Work out a dilemma on some subject of debate. 

5. Examine the following arguments : — 

(1) It is either raining or not raining; it is not raining; 
therefore it is raining. 

1 Aikins. 



322 QUESTIONS AND EXERCISES 

(2) No honest man can advocate a change in the 
creed of his church; for he must either believe it 
or not believe it; and if he believes it, he cannot 
honestly help to change it, while if he does not 
believe it he cannot honestly belong to the church 
at all. 

(3) In order to move, a body must move either in the 
place where it is or in the place where it is not. 
But it cannot move in the place where it is, since 
that place is already occupied. Neither can it 
move in the place where it is not. Motion is there- 
fore impossible. 

(4) If transportation is not felt as a severe punishment, 
it is in itself ill-suited to the prevention of crime; 
if it is so felt, much of its severity is wasted, from 
its taking place at too great a distance to affect 
the feeling, or even come to the knowledge, of most 
of those whom it is designed to deter; but one or 
the other of these must be the case; therefore trans- 
portation is not calculated to answer the purpose 
of preventing crime. 

CHAPTER XIV 

1. Distinguish between a 'sophism' and a 'fallacy.' 

2. Review the formal fallacies. 

3. Be able to classify material fallacies under two appro- 
priate headings. 

4. Look up advertisements to see whether you can find 
some examples of amphiboly. 

5. Give an example of the fallacy of accident. Also of the 
converse fallacy of accident. 

6. Explain the difference between 'begging the question' 

and 'irrelevant conclusion.' 

7. Give an example each of Argumentum ad hominem, Ar- 
gumentum ad populum, Argumentum ad ignorantiam, 
and Argumentum ad vericundiam. 

8. Note and classify the fallacies in the following argu- 
ments : — 

(1) A monopoly of the sugar-refining business is bene- 
ficial to the sugar-refiners; and of the corn trade to 



QUESTIONS AND EXERCISES 323 

the corn-growers; and of silk manufacture to the 
silk-weavers; and of labor to the laborers. Now, 
all these classes of men make up the whole com- 
munity. Therefore a system of restrictions upon 
competition is beneficial to the community. 1 

(2) Any student in college would stand higher in his 
class if he received higher marks; hence, if all 
marks were raised ten per cent every man would 
stand nearer the head of his class. 

(3) Since attending that mass meeting of students, I 
have had no confidence in decisions reached in 
that way. 

(4) Wine is a stimulant; therefore, in every case where 
a stimulant is harmful, wine is harmful. 

(5) We know that God exists, because the Bible tells 
us so; and we know that whatever the Bible affirms 
is true, because it is of divine origin. 

(6) A miracle is incredible because it contradicts the 
laws of nature. 

(7) We charge him (King Charles the Second) with 
having broken his coronation oath, and we are 
told that he kept his marriage vows; we accuse 
him of having given up his people to the merciless 
infliction of the most hot-headed and hard-hearted 
of prelates, and the defense is that he took his little 
son on his knee and kissed him; we censure him for 
having violated the articles of the Petition of 
Rights, after having for a good and valuable con- 
sideration promised to observe them, and we are 
informed that he was accustomed to hear prayers 
at six o'clock in the morning. 

What fallacy does Macaulay refer to in this 
passage? 2 

(8) If it is fated that you die, you will die whether 
you call in a doctor or not, and if it is fated that 
you will recover, you will recover whether you call 
in a doctor or not. But it must be fated either that 
you die or that you recover. Therefore, you will 
either die or recover, whether you call in a doctor 
or not. 

1 Hyslop. l Russell. 



324 QUESTIONS AND EXERCISES 

(9) Every incident in the narration is probable; hence, 
the narrative is probable. 
(10) The growing size of London bodes evil to England 
because London is the heart of England, and a 
swollen heart is a sign of disease. 
9. "The President of the United States can veto bills, but 
he can only veto a bill as a whole. It is therefore not 
uncommon for Congress to tack on to a bill which the 
President feels bound to pass a clause containing a 
measure to which it is known that he objects." Show 
that this is a practical application of a fallacy. 

10. "One of the most remarkable examples of fallacy is 
furnished by the political theory of Hobbes and Rous- 
seau, known as the theory of the 'social compact.' We 
are supposed bound by the promise entered into by our 
ancestors before society was called into existence; but 
there is no such thing as an obligatory promise until so- 
ciety has been formed." What important assumption is 
made in this criticism of the compact-theory? 

11. "How is it that we hear so much of French immorality, 
and nothing, or next to nothing, of Italian? How is it 
that, in France, we have heard so much of English bar- 
barity and cruelty, whilst the accounts of Turkish 
cruelty were received with the smile of incredulity or 
the shrug of indifference?" * What tendency to fallacy 
does this quotation illustrate? Give other instances. 

12. "Achilles and a tortoise run a race together. Achilles 
runs ten times quicker than the tortoise, and accepts, in 
consequence, a handicap of a hundred yards. Under these 
conditions, argued Zeno, Achilles will never overtake the 
tortoise; for when the tortoise has gone ten yards, Achilles 
will still be ten yards behind him. When these ten 
yards are caught up, the tortoise will still be ahead by 
one yard. When this yard is caught up, one-tenth of a 
yard will still separate them, and so on indefinitely. 
Achilles, then, though he will be continually drawing 
nearer to the tortoise, will never actually overtake him." 
How would you criticize this argument? 

1 Hammerton, French and English. 



QUESTIONS AND EXERCISES 325 

FURTHER EXAMPLES OF DEDUCTIVE 
ARGUMENTS 

CHAPTERS X TO XIV 

1. The right should be enforced by law; the exercise of the 
suffrage is a right, and should therefore be enforced by 
law. 

2. Every rule has exceptions; this is a rule, and therefore 
has exceptions; therefore there are some rules that have 
no exceptions. 

3. Is a stone a body? Yes. Then is not an animal a body? 
Yes. Are you an animal? I think so. Ergo, you are a 
stone, being a body. 

4. His imbecility of character might have been inferred 
from his proneness to favorites; for all weak princes 
have this failing. 

5. At the time of the Galveston flood men worked sixteen 
hours a day; hence, to talk of an eight-hour day as a 
necessity for the working classes is absurd. 1 

6. Haste makes waste, and waste makes want; therefore 
a man never loses by delay. 

7. A college education does not pay for most self-made 
Americans have succeeded without it. 

8. All material bodies impress the senses; mind does not 
impress the senses. What is the inference? 2 

9. Art is not fostered by money ; for a true artist would prac- 
tice his art for its own sake, and a bad artist should not 
be encouraged. 

10. Wealth is in proportion to value, value to efforts, efforts 
to obstacles; therefore wealth is in proportion to ob- 
stacles. 

11. For those who are bent on cultivating their minds by 
diligent study, the incitement of academic honors is 
unnecessary; and it is ineffectual for the idle and such 
as are indifferent to mental improvement; therefore the 
incitement of academic honors should be abolished. 

12. It is impossible to be a good shot without having a 

1 Jones. 2 Tavlor. 



326 QUESTIONS AND EXERCISES 

steady hand; John has a steady hand; he is capable, 
therefore, of becoming a good shot. 
IS. The theory of evolution is not true, for it was not ac- 
cepted by Agassiz or by Gladstone; moreover, you cannot 
accept this doctrine, for it is disclaimed by the au- 
thorities of your church. 1 

14. The end of a thing is its perfection; death is the end of 
life; therefore death is the perfection of life. 

15. Improbable events happen almost every day; but what 
happens almost every day is a very probable event; 
therefore improbable events are very probable events. 

16. No evil should be allowed that good may come of it; all 
punishment is an evil; therefore no punishment should 
be allowed that good many come of it. 

17. Why does a ball, when dropped from the masthead of a 
ship in full sail, fall, not exactly at the foot of the mast, 
but nearer to the stern of the vessel? 

18. Written examinations are not absolutely fair tests of a 
student's scholarship — much less of his industry and 
intelligence. It is therefore wrong to base his grade 
upon them. 

19. A vacuum is impossible, for if there is nothing between 
two bodies they must be in contact. 

20. "They tell us that we are weak, unable to cope with so 
formidable an adversary; but when shall we be stronger? " 

21. Nothing is better than wisdom; dry bread is better than 
nothing; therefore dry bread is better than wisdom. 

22. Whoever believes this is a heretic; so that you are no 
heretic, for you do not believe this. 

23. If a man is educated, he does not want to work with his 
hands; consequently, if education is universal, industry 
will cease. 

24. M The railroads have usually acted upon the apparent pol- 
icy that it is none of the public's business whether they 
are overcapitalized or not. It remained for the counsel 
for the N. and N. Railroad, a road notorious for its 
stock-watering operations, publicly to declare — in form 
of a question, it is true, but none the less bluntly — the 
railroad position. If the N. and N. 'charges reasonable 
rates,' demands its counsel, 'what is it to the public 

1 Creighton. 



QUESTIONS AND EXERCISES 327 

whether its capitalization be high or low?'" What 
assumption is involved in this question? 1 

25. Berkeley's Theory of the Non-Existence of Matter is 
palpably absurd, for it is impossible even to place one's 
foot on the ground without experiencing the resistance 
of matter. 

26. I have no hesitation in saying that the proposition, how- 
ever good in theory, is in practice utterly absurd. 

27. Epimenides the Cretan says that "all Cretans are liars," 
but Epimenides is himself a Cretan; therefore he is him- 
self a liar. But if he be a liar, what he says is untrue, and 
consequently the Cretans are veracious; but Epimenides 
is a Cretan, and therefore what he says is true; hence the 
Cretans are liars, Epimenides is himself a liar, and what 
he says is untrue. Thus we may go on alternately 
proving that Epimenides and the Cretans are truth- 
ful and untruthful. 

28. There exist many differences of opinion and much un- 
certainty with regard to many questions connected with 
geology; consequently geology is not a science, and any 
arguments which assume the truth of geological theories 
must invariably be regarded with considerable sus- 
picion. 

29. Personal deformity is an affliction of nature; disgrace is not 
an affliction of nature; personal deformity is not a disgrace. 

SO. Testimony is a kind of evidence which is very likely to be 
false; the evidence on which most men believe that 
there are pyramids in Egypt is testimony; therefore the 
evidence on which most men believe that there are pyra- 
mids in Egypt is very likely to be false. 

31. Why should any but professional moralists trouble them- 
selves with the solution of moral difficulties? For, as 
we resort to a physician in case of any physical disease, 
so, in the case of any moral doubt or any moral disor- 
ganization, it seems natural that we should rely on 
the judgment of some man especially skilled in the 
treatment of such subjects. 

32. "A asserts with incorrigible optimism that 'without too 
much you cannot have enough of anything. Lots of 
inferior books, lots of bad statues, lots of dull speeches, 

i Bode. 



328 QUESTIONS AND EXERCISES 

of tenth-rate men and women, as a condition of the few- 
precious specimens in either kind being realized/ As 
the condition, yes; but as the cause, no. We can never 
have the precious things in literature merely by adding 
to the multitude of cheap things/' x 

33. "An abundant stream divides two limits of one prop- 
erty . . . and over this stream stood a bridge; and at 
the head of it a gallows, over which were appointed four 
judges to decide according to the law established by the 
lord of the stream, the bridge, and the territory. The 
law ran in this wise: 'If any one shall pass over this 
bridge from one side to the other, he must first swear as 
to whence he comes and on what business he is bound, 
and if he swear truly, he must be allowed to go; but if 
he swear falsely, he shall on that account die by hanging 
on the gallows which is there; and that without remis- 
sion whatever.' This law and its stern conditions being 
known, many went over; and as soon as it was perceived 
that they swore truly, the judges allowed them to pass 
freely. It happened, however, that on swearing one 
man, he took the oath and declared that he was going 
to die on that gallows, and that he had no other business. 
The judges consulted the terms of the oath, and said: 
'If we allow that man to go free, he has sworn falsely, and 
according to the law he ought to die; and if we hang him, 
the oath that he was going to hang on that gallows was 
true, and according to the same law he ought to be free.' " 2 

34. We must either gratify our vicious propensities, or re- 
sist them; the former course will involve us in sin and 
misery; the latter requires self-denial; therefore we must 
either fall into sin and misery or practice self-denial. 

35. "America has still a long vista of years stretching before 
her in which she will enjoy conditions far more auspi- 
cious than any European country can count upon. And 
that America marks the highest level, not only of ma- 
terial well-being, but of intelligence and happiness, 
which the race has yet attained, will be the judgment of 
those who look, not at the favored few for whose bene- 
fit the world seems hitherto to have framed its institu- 
tions, but at the whole body of the people." 3 

1 Creighton. 2 From Don Quixote. 3 James Bryce. 



QUESTIONS AND EXERCISES 329 

36. This is a party measure and therefore we must vote for it. 

37. "Philosophy bakes no bread." Then why waste time 
upon it? 

38. I oppose this bill because it involves an infringement of 
the rights of the liberty-loving citizens of this State. 

CHAPTER XV 

1. Why are 'induction' and "deduction* somewhat mis- 
leading terms? 

2. Show how the perspective of logic has shifted from age 
to age. 

3. Distinguish between the 'logic of consistency' and the 
'logic of investigation.' 

4. Look up an instance of systematic investigation, such 
as can be found in Darwin, Newton, Faraday, etc., and 
analyze the various logical steps taken. 

5. What are the three elements which can be distinguished 
in investigation? 

6. What is involved in generalization? Exemplify the pas- 
sage from the particular to the general. 

7. What is meant by an 'internal relation'? How does the 
relation between a sign and that which it signifies differ 
from association? 

8. Do animals generalize? 

9. Discuss the statement, assigned to Wundt, that "ani- 
mals never reason and man seldom." 

10. Is the tendency to test generalizations as characteristic 
of man as the tendency to generalize itself? 

CHAPTER XVI 

1. What do you understand by science? What are some of 
its guiding ideals? 

2. Look up the history of some science with which you are 
fairly familiar, and ask yourself what its growth consists 
in. 

3. Why is analysis so basic for science? 

4. Point out the significance of technique and instru- 
ments. Are they, in your opinion, sometimes overesti- 
mated at the expense of mental factors? 



330 QUESTIONS AND EXERCISES 

5. What is the nature of experimentation? Indicate the 
advantages of experimentation as against passive ob- 
servation. 

6. Find and analyze at least two important experiments in 
each of the following sciences : physics, chemistry, biology, 
and psychology. 

7. What other methods have grown up in modern investi- 
gation? 

8. What reaction has science had upon common-sense 
thinking? 

9. Become acquainted with the mental life of at least one 
great scientist. 

CHAPTER XVII 

1. What principle should guide induction? 

2. What is meant by 'mere speculation,' and why is it con- 
demned? 

3. State some of the mental and physical conditions of ac- 
curate observation. 

4. Show that perception is a process involving associated 
ideas as well as sensations. 

5. What are the causes of mal-observation and non-ob- 
servation in the following cases? 

(1) A straight stick partly immersed in water seems to 
be bent. 

(2) The sun seen through a fog sometimes appears 
red. 

(3) Patients often seem to feel pain in amputated 
limbs. 

(4) A rearrangement of the furniture in a room is often 
unnoticed. 

(5) There are marked differences in what the ordinary 
good observer, the artist, and the botanist see in 
a flower. 

(6) Silas Marner mistook Erne's hair for the lost gold. 

(7) Looking at one's watch and not knowing the time 
a moment later. 

(8) Shooting a man for a deer when hunting in the 
woods. 1 

» Jones. 



QUESTIONS AND EXERCISES 331 

6. Seek for cases of erroneous perception in your own ex- 
perience, and try to explain them. 

7. Is memory a direct intuition of the past? 

8. How do the sciences try to eliminate errors due to 
memory? Why cannot this be done in the courts of law? 

9. Present at least five instances of erroneous memory. 
10. How is the relevancy of facts determined? 

CHAPTER XVIII 

1. What is an hypothesis? And what are its conditions? 

2. Show by examples that hypotheses always arise in answer 
to problems. 

3. Criticize the Baconian view of science. 

4. What do men like Ernst Mach and Wilhelm Ostwald 
mean by hypotheses when they are inclined to urge 
scientists to avoid them so far as possible? 

5. Take any two instances of hypotheses which have be- 
come accepted theories and show that only the expert 
could have thought of them. 

6. Distinguish between the 'intuitive' and the 'reflective* 
type of mind. Are these types easily recognizable in 
practice? 

7. Name three famous men who represent, on the whole, 
the intuitive type, and three who are quite clearly of the 
reflective type. 

8. What is the relation between observation and the pos- 
session of an hypothesis? 

9. Explain the nature of the development of an hypothesis. 
Why does such development require systematic knowl- 
edge? 

10. Is a barren hypothesis the same as an un verifiable one? 

11. Distinguish between 'proof and 'verification/ 

12. Why is analogy such an important source of hypotheses? 

13. What is meant by 'false analogy'? Give at least five 
examples. 

14. Take any two important theories generally accepted 
to-day and study their history. Exactly what was the 
problem which they were developed to explain? 

15. What danger is there in arguing from the assumption 
that society is an organism? 



332 QUESTIONS AND EXERCISES 

CHAPTER XIX 

Analyze the following examples of inductive argumenta- 
tion, and state the method implied. Do the facts seem to you 
to be sufficient to found a rule upon? 

1. It maybe a coincidence merely; but, if so, it is remark- 
ably strange that while the chloroform has not changed, 
while the constitutions of the patients have not changed, 
where the use of the inhaler is the rule, there are fre- 
quent deaths from chloroform; whilst in Scotland and 
Ireland, where the use of the inhaler is the exception, 
deaths are proportionally rare. 1 

2. Sir Charles Lyell, by studying the fact that the river 
Ganges yearly conveys to the ocean as much earth as 
would form sixty of the great pyramids of Egypt, was 
enabled to infer that the ordinary slow causes now in 
operation upon the earth would account for the immense 
geological changes that have occurred, without having 
recourse to the less reasonable theory of sudden catas- 
trophes. 

3. Take a bottle of charged water, slightly warmer than 
a given temperature registered by the thermopile, and 
mark the deflection it causes. Then cut the string 
which holds it and the cork will be driven out by 
the elastic force of the carbonic acid gas. The gas 
performs its works, and in so doing it consumes heat 
and the deflection of the thermopile shows that the 
bottle is cooler than before, heat having been lost in 
the process. 

4. Any one who examines the records will soon find out for 
himself that those students who 'scatter' most in their 
choice of studies are those who accomplish least in any 
of them; and when he sees this he ought to realize the 
harm that can be done by a system of absolutely free 
electives. 2 

5. It was a general belief at St. Kilda that the arrival of a 
ship gave all the inhabitants colds. Dr. John Campbell 
took pains to ascertain the fact and to explain it as the 
effect of effluvia arising from human bodies; it was dis- 

1 Creighton. a Aikins. 



QUESTIONS AND EXERCISES 333 

covered, however, that the situation of St. Kilda renders 
a northeast wind indispensably necessary before a ship 
can make a landing. * 

6. The great famine in Ireland began in 1845 and increased 
until it reached a climax in 1848. During this time agra- 
rian crime increased very rapidly until, in 1848, it was 
more than three times as great as in 1845. After this it 
decreased with the return of better crops until, in 1851, 
it was only fifty per cent more than in 1845. It is evi- 
dent from this that a close relation of cause and effect 
exists between famine and agrarian crime. 

7. Wages in the United States are higher than in England, 
because the former country is a republic and has a pro- 
tective tariff. 

8. In Sir Humphry Davy's experiments upon the de- 
composition of water by galvanism, it was found that, 
besides the two components of water, oxygen and hydro- 
gen, an acid and an alkali were developed at the two 
opposite poles of the machine. The insight of Davy 
conjectured that there might be some hidden cause of 
this portion of the effect: the glass containing the water 
might suffer partial decomposition, or some foreign 
matter might be mingled with the water, and the acid and 
alkali be disengaged from it, so that the water would 
have no share in their production. . . . By the substitu- 
tion of gold vessels for glass, without any change in the 
effect, he at once determined that the glass was not the 
cause. Employing distilled water, he found a marked 
diminution of the quantity of acid and alkali evolved; 
yet there was enough to show that the cause, whatever 
it was, was still in operation. . . . He now conceived 
that the perspiration from the hands touching the in- 
struments might affect the case, as it would contain com- 
mon salt, and an acid and an alkali would result from its 
decomposition under the agency of electricity. By care- 
fully avoiding such contact, he reduced the quantity of 
the products still further until no more than slight traces 
of them were perceptible. What remained of the effect 
might be traceable to impurities of the atmosphere, de- 

i Hibben. 



334 QUESTIONS AND EXERCISES 

composed by contact with the electrical apparatus. An 
experiment determined this: the machine was put under 
an exhausted receiver, and, when thus secured from 
atmospheric influence, it no longer evolved the acid and 
the alkali. 1 
9. In a simple fracture of the ribs if the lung be punctured 
by a fragment, the blood effused into the pleural cavity, 
although freely mixed with air, undergoes no decompo- 
sition. That is not the case if air enter directly through 
a wound in the chest. This difference in result must be 
causally connected with special circumstances — viz., 
passage of air through tissues in the lungs. 2 

10. "The two females were then seated upon two chairs 
placed near together, their heels resting on cushions, their 
lower limbs extended, with the toes elevated and the 
feet separated from each other. The object in this ex- 
periment was to secure a position in which the ligaments 
of the knee-joints should be made tense and no oppor- 
tunity offered to make pressure with the foot. We were 
pretty well satisfied that the displacement of the bones 
requisite for the sounds could not be effected unless a 
fulcrum were obtained by resting one foot upon the 
other or on some resisting body. The company, seated 
in a semicircle, quietly waited for the * manifestations' 
for more than half an hour. . . . On resuming the usual 
position on the sofa, the feet resting on the floor, knock- 
ings very soon began to be heard. . . . The conclusion 
seemed clear that the Rochester knockings emanate 
from the knee joint." 3 

11. Give two examples for each of the methods, preferably 
from ordinary experience rather than from science. 

12. Show that Mill's Methods imply a large fund of relevant 
knowledge. 

13. Analyze the causal relation in such a way as to bring 
out methods of testing supposed uniformities. 

14. In what way is the Method of Difference an advance 
upon the Method of Agreement? 

1 Gore, The Art of Scientific Discovery. 2 Russell. 

8 Description of the exposure of a spiritualistic seance, quoted by Podmore, and 
adapted by Taylor. 



QUESTIONS AND EXEKCISES 335 

15, By what methods should the following problems be 
investigated? 

(1) An individual becoming sick after a meal. 

(2) The possibility of a connection between rag-weed 
and hay fever. 

(3) The effect of a new tariff upon the prosperity of a 
country. 

(4) Education and the decrease of superstition. 

(5) The relation between mosquitos and malaria. 

(6) Bad eyes and criminality. 

(7) A crime and the arrest of a suspected person. 

(8) The rapidity of growth of trees and the kind of 
soil. 

(9) Poverty and tuberculosis. 

(10) The effect of radium upon cancer. 

CHAPTER XX 

1. When are statistics resorted to? How do they enable us 
to grasp a field which would otherwise be unmanage- 
able? 

2. Why is definition of the problem and of the terms used 
so important? 

3. Name the stages of any thorough statistical investiga- 
tion. What are the special dangers confronting each of 
these stages? 

4. State the law of statistical regularity, and try to explain 
its foundation. 

5. In what sciences are statistics of greatest significance? 
Why? 

6. Look up cases of erroneously interpreted statistics and 
show wherein the error lies. 

7. "In Sweden the population and the smallpox mortality 
have both been known year by year since 1774. Before 
vaccination the mortality from smallpox for thirty years 
averaged 2045 per million. With permissive vaccination 
from 1802 to 1816 it was reduced to 480; during seventy- 
seven years of compulsory vaccination the mortality 
averaged 155 per million; and for ten years ending 1894 
it has been down to 2 per million. . . . 



336 QUESTIONS AND EXERCISES 

"If we compare the rate of smallpox mortality in the 
different countries, we see an enormous difference be- 
tween the well vaccinated and the badly vaccinated 
populations. Here is a table, given by Dr. Edwardes, of 
the mortality rates per million in the five years 1889 to 
1893: — 

Smallpox 

mortality 

per million 

Germany 2.3 

England and Wales 13.6 

Chief French towns 147. 6 

Italy. 180.8 

Belgium 253 

Austria 313 

Spain 638 

Russia, three years only, including Asi- 
atic Russia 836 

"In Germany, vaccination and revaccination are both 
compulsory. In the other countries revaccination was, 
at that time at least, nowhere enforced." * 

8. "More men than women die every year. This is due to 
the greater mortality attending the life of the male." 2 
What does this mean? How can it be possible? "In 
Germany 109 men die each year for every 100 women." 
What can we conclude from this? Why is it better to 
know that in Germany 28.6 out of every thousand males 
die each year and 25.3 out of every thousand females? 
Since everybody must die sooner or later how is it possible 
that there should be in any country (or in the whole 
world) a permanently greater death-rate for one sex 
than for the other? 

9. Show the importance of the qualitative side of social 
phenomena. Why are quantitative data apt to be mis- 
leading in certain fields? 

i Edinburgh Review, vol. 189, pp. 350-52. 
2 Mayo-Smith, Statistics and Sociology. 



QUESTIONS AND EXERCISES 

10. Interpret the following statistics: — 

A table giving the percentage of accidents occurring 
according to the time of the day 



337 



Time 


Germany 


Italy 


12- 3 a.m. 


1.93 


1.09 


3- 6 a.m. 


2.55 


2.47 


6-9 A.M. 


13.87 


15.40 


9-12 A.M. 


28.42 


29.20 


12-3 p.m. 


13.81 


14.55 


3-6 p.m. 


26.62 


26.48 


6-9 p.m. 


9.25 


7.83 


9-12 p.m. 


3.85 


2.54 



11. Study carefully some one chapter of Mayo-Smith's Statis- 
tics and Sociology with especial attention to the reflective 
analysis which he gives at the end of the chapter. 

12. What statistical investigations would seem to you very 
important for a modern, democratic society? 

13. In the United States census of 1890, the question of 
color — whether black, mulatto, quadroon, or octoroon 
— was asked. Why was such a question faulty from the 
standpoint of statistics? 

14. Point out the sociological bearing of the following statis- 
tics from the United States Life Tables: Of 100,000 
negro females, 18,507 die before the age of one year, 
while of 100,000 white females, 10, 460 die before reaching 
the same age. 

15. It is undeniable that tenancy is increasing in the United 
States. From the Twelfth Census, we have the follow- 
ing comparison : — 





Total 
number 
of farms 


Number operated by 




Owners 


Cask 
tenants 


Share 
tenants 


1880 


4,008,907 
5,739,657 


2,984,306 
3,713,371 


322,357 
752,920 


702,244 


1900 


1,273,366 







338 QUESTIONS AND EXERCISES 

The Marxian Socialist maintains that this increase 
proves concentration in farming. Does any other ex- 
planation suggest itself to you? 

CHAPTER XXI 

1. Under what conditions can science predict with accu- 
racy the occurrence of particular events? Give concrete 
examples. 

2. Are effects always found when their causes are present? Be 
prepared to defend your answer by means of instances. 

3. What does each of the following propositions mean? 

(1) The child will probably catch the measles. 

(2) The earth will probably grow colder in the distant 
future. 

(3) The probability in favor of a long life for a man 
of his profession is very great. 

4. Distinguish between • probability ' and ' objective chance/ 
How can you harmonize the existence of probability 
with the Principle of the Uniformity of Nature? 

5. Is there any difference between saying that a certain 
horse is the most likely to win the race and saying that 
it is likely to win? l 

6. How should life-insurance statistics be interpreted? Can 
they be made to apply to any one individual? If so, in 
what sense? 

7. What reply can be made to the following? "You say 
that the prisoner is probably guilty. I grant it. But this 
only means that the prisoners in most cases of this sort 
are guilty. It does not mean that this particular prisoner 
has even a touch of guilt. Your very use of the word 
'probable' is a confession that for all you know he may 
be absolutely innocent. How then can you ask the jury 
to condemn him to an awful fate? " 2 

8. Discuss the following statement: "Nine times out of 
ten we can act only on probability." 

9. What is the probability that a die will fall with the same 
side up four times in succession? 

10. What is the probability that you will draw either an 
ace or a five of hearts from a full deck of cards? 

1 Aikins. 2 Aikins. 



QUESTIONS AND EXERCISES 339 

11. "The regularities of the mass have no compelling force 
over the individual." x Against what fallacy is this state- 
ment directed? 



CHAPTER XXII 

1. Give some common examples of the use of an arithmetical 
average. Explain such an expression as the * average 
rate of interest.' 

2. Show that percentage of increase in the population of a 
town or city is a case of arithmetical average. 

3. What average would be of most use for the following? 

(1) The standard size of a manufactured article. 

(2) A stock of hats for a clothing store. 

(3) The physical estimation of a varsity crew. 

(4) The salary of teachers. 

4. Find, or work out, a set of statistics and discover the 
mode and the median. 

5. Examine critically the phrase, * the average man.' What 
danger of misinterpretation lurks behind the phrase? 

6. Why are graphical methods being used so freely at the 
present time? 

7. Find at least five devices for graphical representation in 
common use and compare their effectiveness. 2 

8. Look up cases of graphical representation in the popular 
magazines and make a report upon at least four which 
particularly attracted your attention. 

9. "An average must not be a mere numerical average, for 
that amounts to nothing. It must be a typical average, 
expressive of about what the real condition of things is." 
Explain this statement in the light of the preceding 
chapters. 

CHAPTER XXIII 

1. Contrast * scientific investigation' and * judicial proof 
as regards their methods and social surroundings. 

2. Estimate the following arguments : — 

(1) If you believe in the survival of the fittest, you 
must believe that this old manuscript was one of 

1 Mayo-Smith. * See Brinton on this question. 



340 QUESTIONS AND EXERCISES 

the best of its time, for it is the only one that 
has survived. 

(2) This book is authentic; then why should we not 
believe what it says? 

(3) This text of Cicero dates from the twelfth century 
and that dates only from the fourteenth; then 
why is n't this a better one to go by than that? 

(4) This text has great value for the historian, for it 
was restored at infinite pains, and there is now 
every reason to believe that it is substantially 
correct. 

(5) "Come and have your fortune told by Blank's 
system of palmistry. No man of science has ever 
disputed the claims of this system." l 

3. Take any striking criminal case before the courts and 
work out the circumstantial evidence for and against the 
issue in the way suggested in the text. 

4. What is, in your opinion, the comparative probative 
value of circumstantial and testimonial evidence? 

5. Connect the possibility of a plurality of causes with the 
methods used in explaining events. 

6. What seems to you to be a reasonable doubt? 

7. Examine the following case. Do you think that there 
was a reasonable doubt of Bradford's guilt? 

"Jonathan Bradford, in 1736, kept an inn, in Ox- 
fordshire, on the London road to Oxford. He bore a 
very exceptional character. Mr. Hayes, a gentleman 
of fortune, being on his way to Oxford, on a visit to 
a relation, put up at Bradford's. He there joined com- 
pany with two gentlemen, with whom he supped, and, 
in conversation, unguardedly mentioned that he had 
then about him a sum of money. In due time they 
retired to their respective chambers; the gentlemen 
to a two-bedded room, leaving, as is customary with 
many, a candle burning in the chimney corner. Some 
hours after they were in bed, one of the gentlemen, 
being awake, thought he heard a groan in an adjoining 
chamber; and this being repeated, he softly awaked 
his friend. They listened together, and the groans 
increasing, as of one dying and in pain, thev both 

1 Aikins. 



QUESTIONS AND EXERCISES 341 

instantly arose and proceeded silently to the door of 
the next chamber, whence they had heard the groans, 
and, the door being ajar, saw a light in the room. They 
entered, and perceived a person weltering in his blood 
in the bed, and a man standing over him with a dark 
lantern in one hand and a knife in the other! The man 
seemed as petrified as themselves, but his terror car- 
ried with it all the terror of guilt. The gentlemen soon 
discovered that the murdered person was the stranger 
with whom they had that night supped, and that the 
man standing over him was their host. They seized 
Bradford directly, disarmed him of his knife, and 
charged him with being the murderer. He assumed, 
by this time, the air of innocence, positively denied 
the crime, and asserted that he came there with the 
same humane intentions as themselves; for that, hear- 
ing a noise, which was succeeded by a groaning, he 
got out of bed, struck a light, armed himself with a 
knife for his defense, and was but that minute entered 
the room before them. These assertions were of little 
avail; he was kept in close custody till the morning, 
and then taken before a neighboring justice of the 
peace. Bradford still denied the murder, but, never- 
theless, with such apparent indications of guilt, that 
the justice hesitated not to make use of this most ex- 
traordinary expression, on writing out his mittimus, 
'Mr. Bradford, either you or myself committed this 
murder.' " 

8. How does the mind work in passing judgment upon a 

very complex case? Study your own method of reach- 
ing a conclusion in some particular problem of a high 
degree of complexity. 

9. Analyze one of Conan Doyle's Sherlock Holmes stories 

to see just how the circumstantial evidence is used 
both to lead and to mislead. 
10. What is the fallacy of 'neglected factor'? Give at least 
two examples which have come within your experi- 



1 If the teacher can secure the book, he will find many interesting examples for all 
the difficulties confronting evidence in Wigmore's Principles of Judicial Proof. These 
examples are too long to quote in the present text. 



342 QUESTIONS AND EXERCISES 

11. Look up the investigation of some historical myth like 

that of William Tell. What is its interest to the lo- 
gician? 

12. Newton was of the opinion that oral tradition could be 

trusted for eighty years after the event. Others have 
named forty years. Why are such estimations rather 
absurd? 

13. It is asserted by many recent historians of the American 

Revolution that our school histories contain a deal 
of myth along with a fair percentage of fact. What 
causes might lead to legend and myth about the 
founders of the American Republic? 

CHAPTER XXIV 

1. What is the nature of explanation? 

2. Take any two problems which have arisen lately in your 
experience and try to grasp the exact character of the 
explanation given them. 

3. What is meant by the 'sentiment of rationality'? Show 
that it depends upon the constitution of our minds. 

4. Is explanation possible apart from concepts? 

5. Apply Dewey's analysis of the role of concepts to at 
least two cases of interpretation, stressing identification, 
supplementation, and placing in a system. 

6. What difference of setting have the two terms, 'proof 
and 'explanation'? What have they in common? 

7. How are induction and deduction united in the process 
of explanation? Illustrate by examples either from prac- 
tical life or from science. 

8. Are all systems equally tentative? Can you think of any 
system which seems to you to be in final shape? 

9. How would you distinguish between 'general' and 'spe- 
cific' explanation? 

10. What principle would you adopt as a means of arranging 
the sciences in an orderly fashion? Do you think that 
such an ordering of them gives a penetrative classifica- 
tion? 

11. Why is mathematics usually spoken of as 'deductive'? 
Does this seem to you the best term that could be 
used? 



QUESTIONS AND EXERCISES 343 

12. Examine historical investigation in the light of your 
present knowledge of logic. Show especially that all facts 
are judgments. 

CHAPTER XXV 

1. Distinguish clearly between 'consistent thinking' and 
* true thinking.' 

2. What is meant by 'logical necessity'? 

3. State and explain the 'Laws of Thought.' 

4. What principles are implied in all investigation which 
seeks to determine truth? 

5. How would you formulate your conception of the inter- 
nal criteria of truth? 

6. Explain the conception of degrees of belief. Relate your 
views to the modality of judgments. 

7. Does language express adequately the different degrees 
of belief we actually hold? 

8. Show that the meaning of knowledge is intimately bound 
up with the meaning of truth. 

9. Read Tennyson's In Memoriam, xxxiv. Does it seem 
to you to imply an appeal to a standard of truth other 
than the logical? 

10. Be prepared to defend James's position or Clifford's ac- 
cording as the one or the other strikes you as the sounder. 



INDEX 



(Kindly arranged by Mr. Douglas Clapperton) 



Absolute term, 29, 34. 

Abstract sciences, 288. 

Accident, fallacy of, 148. 

Agreement and difference, joint 
method of, 215, 217. 

Agreement, method of, 215, 217. 

Aikins, quoted, 249, 270. 

Ambiguity, 41; causes of, 41. 

Ambiguous terms, fallacy of, 143. 

Amphiboly, 144. 

Analogy, as basis of reasoning, 
208; false, 209. 

Analytic division, 59. 

Apodeictic judgment, 301. 

Argumentum ad Hominem, 153; 
ad ignorantiam, 154; ad popu- 
lum, 153; ad verecundiam, 155. 

Aristotle's definition of syllog- 
ism, 107. 

Arithmetical average, 252, 257. 

Assertions, 76, 79. 

Assertoric judgment, 301. 

Average, geometric, 256, 257; 
median, 256, 257; uses of, 251 ; 
weighted, 253, 257. 

Bain, quoted, 236. 

Belief, degrees of, 301. 

Bode, quoted, 15, 30, 35, 157, 

210, 221, 243, 277. 
Bosanquet, quoted, 85, 197. 
Bowley, quoted, 229, 253. 
Brinton, quoted, 258, 262. 
Burrill, quoted, 265. 

Carhart, quoted, 222. 
Cartograms, 257. 



Categorematic words, 28. 

Cause, definition of, 211. 

Certainty, possibility of, in fore- 
casting events, 240. 

Change in meaning of words, 
44. 

Circumstantial evidence, 265; 
nature of, 267; circumstantial 
and testimonial evidence, 266. 

Classes, 51; coordination of, 55; 
subordination of, 55; super- 
ordination of, 55. 

Classification, artificial, 52, 53; 
definition of, 50; diagnostic, 
53; index, 53; natural, 52, 53. 

Classificatory division, 60. 

Clifford, quoted, 309, 310. 

Collective terms, 33. 

Complex question, 151. 

Composition, fallacy of, 144. 

Concepts, 20, 96; use of, in 
explanation, 280. 

Concomitant variations, method 
of, 221. 

Concrete logic, 5. 

Concrete sciences, 290, 291. 

Concrete term, 30. 

Conditions and occasions of 
thought, 15; personal condi- 
tions, 17. 

Connotation, 37, 38. 

Consistent thinking, nature of, 
294; relation to truth, 294. 

Constancy of averages, 233, 245. 

Constituent species, 57. 

Contradiction, law of, 207. 

Contradictories, 100. 



346 



INDEX 



Contraries, 100. 

Conversion, 102; by contraposi- 
tion, 105; by limitation, 102; 
simple, 102. 

Coordinate species, 57. 

Copula, 28. 

Correlatives, 34. 

Creighton, quoted, 34, 137. 

Darwin, quoted, 192; from 
Creighton, 204. 

Davidson, quoted, 44, 62, 69. 

Definition, nature of, 64; pur- 
pose of, 63, 64; definition and 
classification, 66. 

Definition of logic, 1. 

Denotation, 37, 38. 

Dewey, quoted, 11, 169, 176, 
178, 203, 279, 282. 

Dichotomous division, 58, 59. 

Dictum, 301. 

Difference, method of, 219. 

Differentia, 57. 

Dilemma, 137. 

Direct evidence, 269. 

Discovery and proof, 11. 

Disjunctive syllogism, 136. 

Distribution of terms, 94. 

Division, 56. 

Division, fallacy of, 145. 

Doubt, logic of, 309. 

Empirical logic, 5. 
Enthymeme, 126. 
Episyllogisms, 127. 
Equivocal words, 43. 
Erroneous perception, cause of, 

189. 
Events, prediction of, 239. 
Evidence, convergence of, 268; 

fallacies in weighing evidence, 

275. 
Exceptive proposition, 93. 
Excluded middle, law of; 297. 
Exclusive propositions; 93. 



Experimentation, 177; in biol- 
ogy, 179; in psychology, 180. 

Explanation, general, 287; levels 
of, 285; nature of, 278; and 
proof, 282; specific, 287. 

Extension, 37. 

Extra-syllogistic reasoning; 129. 

Fact, theory and, 24, 25. 
Facts, 194; relevant, 195. 
Fallacies, 141; classification of, 

142; deductive, 142. 
Fallacy, of four terms, 112; 

of unwarranted assumption, 

149. 
Figure of speech, fallacy of, 

148. 
Figures of the syllogism, 118. 
Frequency graphs, 262. 
Fundamentum divisionis, 57. 

General term, 32. 

Genus, 56. 

Geometric average, 256, 257. 

Gibson, quoted, 144, 146, 149, 
152. 

Giffen, quoted, 230. 

Graphs, cartogram, 257; fre- 
quency, 262; and graphical 
methods, 257; pictogram, 258. 

Gross, quoted, 271. 

Helmholtz, quoted, 286. 

Hibben, quoted, 54, 237. 

Historical science, 290, 291. 

History of logic, 160. 

Huxley, quoted, 199. 

Hypotheses, definition of, 197; 
development of, 205 ; function 
of, 182; kinds of, 198; origin 
of, 200; proof of, 206; value 
of, 203; hypothesis, theory 
and fact, 207. 

Hypothetical syllogism, 132; 
rule of, 134. 



INDEX 



347 



Identity, law of, 296. 
Immediate inference, 98. 
Indefinite propositions, 90. 
Induction and deduction, 159. 
Inductive logic, 5. 
Inertia of large numbers, law of, 

233. 
Inferential element in precepts, 

21. 
Infimse species, 57. 
Intention, 37. 
Introductory logic, 5. 
Intuitive mind, 202. 
Irrational evidence, fallacy of, 

152. 
Irrelevant conclusion, 156. 

James, quoted, 23, 180, 204, 

297, 304, 305, 306, 307. 
Jevons, quoted, 54, 148, 177, 

189, 226, 242. 
Jones, quoted, 66 , 104, 128, 223, 

249, 272. 
Joseph, quoted, 3, 4, 60, 130, 

146, 286, 289. 
Judgment, 27; and concepts, 81; 

definition of, 84; levels of, 80; 

relation of, to knowledge, 84. 
Judicial proof, 264; difficulties 

confronting, 265. 

Kinds of logic, 4. 
King, quoted, 228, 229, 230, 
234, 248, 252, 256. 

Langlois and Seignobos, quoted, 
290, 292. 

Language, 48; law of, in logic, 6; 
purpose of, 87. 

Law of contradiction, 297; of 
excluded middle, 297; of iden- 
tity, 296; of language, 6. 

Laws of thought, 296. 

Legal reasoning, 264. 

Locke, quoted, 63, 108, 152, 155. 



Lodge, quoted, 16. 

Logic, definition of, 1; as ap- 
plied science, 3; kinds of, 4; 
value of, 2; concrete, 5; em- 
pirical, or inductive, 5; intro- 
ductory, 5; material of, 7; 
relation of, to other sciences, 
6; symbolic, 5; of systematic 
investigation, 159. 

Lotze, quoted, 147. 

McDougall, quoted, 179. 

Macleane, quoted, 48, 71, 73. 

Major term, 11. 

Material of logic, 7. 

Mayo-Smith, quoted, 232. 

Meaning of terms, 38. 

Measurement, importance of, 
177. 

Median, 256, 257. 

Mellone, quoted, 219. 

Memory, errors of, 192. 

Middle term, 110. 

Mill, quoted, 208, 226. 

Mill's methods of testing con- 
nections, 214; method of 
agreement, 215; of difference, 
219. 

Minor term, 111. 

Minto, quoted, 47, 48, 92, 107, 
124, 162, 217, 233. 

Mode, 255, 257. 

Modus ponens, 133; tollens, 133. 

Moods, of syllogisms, 118. 

Multiple working hypotheses, 
method of, 205. 

Miinsterberg, quoted, 186, 188. 

Negative correlation, 236. 
Negative term, 56. 
Non-sequitur, 157. 

Observation, conditions of, 185. 

Ob version, 103. 

Opposition of propositions, 99. 



348 



INDEX 



Partitive propositions, 93. 

Percept, definition of, 20, 21; 
inferential element in, 21. 

Perception, errors in, 187. 

Petitio principii, 149. 

Pictograms, 258. 

Pillsbury, quoted, 13, 19, 52, 283. 

Positive term, 36. 

Post hoc, ergo propter hoc, 212. 

Postulates of logic, 298. 

Predicables, 73. 

Preindesignate propositions, 90. 

Privitive term, 37. 

Probabilities, mistakes in inter- 
pretation of, 248. 

Probability, meaning of, 240; 
empirical, 242; based on aver- 
ages, 243; and chance, 241; 
contrasted with certainty, 
241; estimating kinds of, 242; 
probability in regard to 
events, 241; in regard to 
principles, 241. 

Problem of generalization, 167. 

Problematic judgment, 301. 

Processes preliminary to reflec- 
tive thought, 20. 

Proof, and explanation, 282; and 
discovery, 11. 

Propositions, 27, 76, 98, cate- 
gorical, 89; disjunctive, 89; 
hypothetical, 89; quality of, 
89; quantity of, 89. 

Prosyllogisms, 127. 

Proximum genus, 57. 

Psychologist's view of reason- 
ing, 13. 

Quality of propositions, 89, 90. 
Quantity of propositions, 89, 90. 
Quetelet, quoted, 245. 

Real definition, 64. 
Reasoning, examples of, 14; 
psychologist's view of, 13. 



Reflective mind, 202. 

Reflective thought, processes 
preliminary to, 20. 

Relation of logic to other sci- 
ences, 6. 

Relative term, 34. 

Residues, method of, 224. 

Ribot, quoted, 201, 202. 

Romanes, quoted, 23. 

Rules, of definition, 69-71; of 
division, 58; for mathematical 
probability, 246; of syllogism, 
112. 

Russell, quoted, 284 

Schiller, quoted, 117. 

Science, development of, 173; 
method of graphs in, 181; 
statistical method in, 180. 

Scientific investigation, 264. 

Sellars, quoted, 305. 

Setting of thought, 17. 

Sidgwick, quoted, 3, 25, 51, 68, 
209, 214. 

Sigwart, quoted, 278. 

Singular term, 30, 31. 

Smith, quoted, 44. 

Sociology of logic, 16. 

Socratic dialectic, 67. 

Sorites, 128; Aristotelian, 128; 
Goclenian, 129. 

Species, 56. 

Square of opposition, 100. 

Statistical investigation, stages 
in, 230. 

Statistical regularity, law of, 
232. 

Statistics, definition of, 229; in 
causal relations, 236; dangers 
in use of, 233; inertia of large 
numbers, 233; value of, 235. 

Steps in systematic investiga- 
tion, 166. 

Stout, quoted, 40. 

Subalterns, 100. 



INDEX 



349 



Subcontraries, 100. 

Summum genus, 57. 

Syllogism, axiom of, 110; de- 
fined, 107; disjunctive, 136; 
elements of, 110; figures of, 
118; function of, 162; hypo- 
thetical, 132; moods of, 118; 

r nature of, 107; rules of, 112. 

Symbolic classification of propo- 
sitions, 91. 

Symbolic logic, 5. 

Syncategorematic words, 28. 

Synthetic classification, 59. 

Systems of knowledge, typical, 
288. 

Systems, tentative nature of, 283. 

Taylor, quoted, 56, 154. 
Technique and instruments, 

value of, 175. 
Terms, 27, 28. 

Testimonial evidence, 266, 269. 
Testimony, definition of, 270; 

critical attitude toward, 270; 

errors in, 193; logical tests of, 

273. 
Theory and fact, 24, 25. 
Thinking, definition of, 18; 

purpose of, 18. 



Thought, conditions and occa- 
sions of, 15; laws of, 296; 
setting of, 17; what is, 10. 

True idea, definition of, 303. 

Truth, 298; criteria of, 299; 
definitions of, 304; meaning 
of, 303; pragmatic definition 
of, 304; truth and validity, 
299; and will to believe, 305. 

Tyndall, quoted, 200. 

Uniformity of nature, principle 

of, 170. 
Uni vocal words, 43. 

Vagueness, 46; of abstract 

terms, 47. 
Value of logic, 2. 
Verbal definition, 64. 
Verification, 300. 
Vincent, quoted, 291. 

Weighted average, 253, 257. 
Welton, quoted, 198, 246, 247. 
Whately, quoted, 156. 
Whewell, quoted, 8. 
Whitehead, quoted, 289. 
Wigmore, quoted, 270, 271, 
274. 



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